Q&A Hero

Q: A simple gyroscope consists of a wheel (R= 0.75 m,I= 0.9 MR2) rotating on a horizontal shaft. If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel? A) 1.9 x 10-2rad/s B) 2.9 x 10-2rad/s C) 0.19 rad/s D) 0.28 rad/s E) cannot be calculated without knowing the mass of the wheel

Q: A simple gyroscope consists of a wheel (M= 2.0 kg, R= 0.75 m, I= 1.1 kgm2) rotating on a horizontal shaft. If the shaft is balanced on a pivot 0.50 m from the wheel, and the wheel rotates at 500 rev/min, what is the precession frequency of the wheel? A) 1.8 x 10-2rad/s B) 2.7 x 10-2rad/s C) 0.17 rad/s D) 0.26 rad/s E) 0.50 rad/s

Q: What is precession? A) Precession is the action of a solid rolling up a slope, prior to rolling back down again. B) Precession is the increase in economic activity before a recession. C) Precession is the rotation of a solid around a fixed axis. D) Precession is the rotation of an angular momentum vector around a vertical axis. E) Precession is the oscillatory motion of an angular momentum vector as it rotates around a vertical axis.

Q: A block with mass M,on the end of a string, moves in a circle on a horizontal frictionless table as shown. As the string is slowly pulled through a small hole in the table: A) the angular momentum of Mremains constant B) the angular momentum of Mdecreases C) the kinetic energy of Mremains constant D) the kinetic energy of Mdecreases E) none of the above

Q: A particle, held by a string whose other end is attached to a fixed point C, moves in a circle on a horizontal frictionless surface. If the string is cut, the angular momentum of the particle about the point C: A) increases B) decreases C) does not change D) changes direction but not magnitude E) none of these

Q: Two pendulum bobs of unequal mass are suspended from the same fixed point by strings of equal length. The lighter bob is drawn aside and then released so that it collides with the other bob on reaching the vertical position. The collision is elastic. What quantities are conserved in the collision? A) Both kinetic energy and angular momentum of the system B) Only kinetic energy C) Only angular momentum D) Angular speed of lighter bob E) None of the above

Q: A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg m2. It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. When the child reaches the rim the angular velocity of the merry-go-round is:A) 0.62 rad/sB) 0.73 rad/sC) 0.77 rad/sD) 0.91 rad/sE) 1.1 rad/s

Q: A playground merry-go-round has a radius R and a rotational inertia I. When the merry-go-round is at rest, a child with mass m runs with speed valong a line tangent to the rim and jumps on. The angular velocity of the merry-go-round is then: A) mv/I B) v/R C) mRv/I D) 2mRv/I E) mRv/(mR2+ I)

Q: A phonograph record is dropped onto a freely spinning turntable. Then: A) neither angular momentum nor mechanical energy is conserved because of the frictional forces between record and turntable B) the frictional force between record and turntable increases the total angular momentum C) the frictional force between record and turntable decreases the total angular momentum D) the total angular momentum remains constant E) the sum of the angular momentum and rotational kinetic energy remains constant

Q: A wheel,with rotational inertia I,mounted on a vertical shaft with negligible rotational inertia, is rotating with angular speed 0. A nonrotating wheel with rotational inertia 2Iis suddenly dropped onto the same shaft as shown. The resultant combination of the two wheels and shaft will rotate at:A) 0 /2B) 20C) 0/3D) 30E) 0 /4

Q: Two disks are mounted on low-friction bearings on a common shaft. The first disc has rotational inertia Iand is spinning with angular velocity . The second disc has rotational inertia 2Iand is spinning in the same direction as the first disc with angular velocity 2 as shown. The two disks are slowly forced toward each other along the shaft until they couple and have a final common angular velocity of:A) 5ï·ï€ /3B) C) D) E) 3

Q: When a woman on a frictionless rotating turntable extends her arms out horizontally, her angular momentum: A) must increase B) must decrease C) must remain the same D) may increase or decrease depending on her initial angular velocity E) tilts away from the vertical

Q: When a man on a frictionless rotating stool extends his arms horizontally, his rotational kinetic energy: A) must increase B) must decrease C) must remain the same D) may increase or decrease depending on his initial angular velocity E) may increase or decrease depending on his angular acceleration

Q: A uniform sphere of radius Rrotates about a diameter with angular momentum of magnitude L. Under the action of internal forces the sphere collapses to a uniform sphere of radius R/2. The magnitude of its new angular momentum is: A) L/4 B) L/2 C) L D) 2L E) 4L

Q: A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating turntable. The effect of the weights is to double the rotational inertia of the system. As he is rotating, the man opens his hands and drops the two weights. They fall outside the turntable. Then: A) his angular velocity doubles B) his angular velocity remains about the same C) his angular velocity is halved D) the direction of his angular momentum vector changes E) his rotational kinetic energy increases

Q: A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms: A) his angular velocity increases B) his angular velocity remains the same C) his rotational inertia decreases D) his rotational kinetic energy increases E) his angular momentum remains the same

Q: An ice skater with rotational inertia I0 is spinning with angular speed 0. She pulls her arms in, thereby increasing her angular speed to 40. Her rotational inertia is then:A) I0B) I0 /2C) 2I0D) I0 /4E) 4 I0

Q: A pulley with radius Rand rotational inertia Iis free to rotate on a horizontal fixed axis through its center. A string passes over the pulley. A block of mass m1 is attached to one end and a block of mass m2,is attached to the other. At one time the block with mass m1is moving downward with speed v. If the string does not slip on the pulley, the magnitude of the total angular momentum, about the pulley center, of the blocks and pulley, considered as a system, is given by:A) (m1- m2)vR+ Iv/RB) (m1+ m2)vR+ Iv/RC) (m1- m2)vR- Iv/RD) (m1+ m2)vR- Iv/RE) none of the above

Q: A uniform disk has radius Rand mass M. When it is spinning with angular velocity about an axis through its center and perpendicular to its face its angular momentum is I. When it is spinning with the same angle velocity about a parallel axis a distance haway its angular momentum is:

Q: A pulley with radius Ris free to rotate on a horizontal fixed axis through its center. A string passes over the pulley. Mass m1is attached to one end and mass m2is attached to the other. The portion of the string attached to m1has tension T1and the portion attached to m2has tension T2. The magnitude of the total external torque, about the pulley center, acting on the masses and pulley, considered as a system, is given by:

Q: Two objects are moving in the x, yplane as shown. If a net torque of 44Nm acts on them for 5.0 seconds, what is the change in their angular momentum? A) 0 kgm2/s B) 6 kgm2/s C) 30 kgm2/s D) 150 kgm2/s E) 220 kgm2/s

Q: A single force acts on a particle P. Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle's angular momentum about the point O, least to greatest. A) 1, 2, 3, 4 B) 1 and 2 tie, then 3, then 4 C) 1 and 2 tie, then 4, then 3 D) 1 and 2 tie, then 3 and 4 tie E) All are the same

Q: A 2.0-kg stone is tied to a 0.50 m long string and swung around a circle at a constant angular velocity of 12 rad/s. The circle is parallel to the xyplane and is centered on the zaxis, 0.75 m from the origin. The magnitude of the torque about the origin is: A) 0 Nm B) 6.0 Nm C) 14 Nm D) 72 Nm E) 108 Nm

Q: A 2.0-kg stone is tied to a 0.50-m long string and swung around a circle at a constant angular velocity of 12 rad/s. The net torque on the stone about the center of the circle is: A) 0 Nm B) 6.0 Nm C) 12 Nm D) 72 Nm E) 140 Nm

Q: A rod rests on frictionless ice. Forces that are equal in magnitude and opposite in direction are simultaneously applied to its ends as shown. The quantity that has a magnitude of zero is its: A) angular momentum B) angular acceleration C) total linear momentum D) kinetic energy E) rotational inertia

Q: A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular momenta after a given time t, least to greatest. A) all tie B) disk, hoop, sphere C) sphere, disk, hoop D) hoop, sphere, disk E) hoop, disk, sphere

Q: A 2.0-kg block starts from rest on the positive xaxis 3.0 m from the origin and thereafter has an acceleration given by in m/s2. The torque, relative to the origin, acting on it at the end of 2.0 s is:A) 0 NmB) (-18 Nm)C) (+24 Nm)D) (-144 Nm)E) (+144 Nm)

Q: A 2.0-kg block travels around a 0.50-m radius circle with an angular speed of 12 rad/s. The circle is parallel to the xyplane and is centered on the zaxis, 0.75 m from the origin. The component in the xyplane of the angular momentum around the origin has magnitude: A) 0 kgm2/s B) 6.0 kgm2/s C) 9.0 kgm2/s D) 11 kgm2/s E) 14 kgm2/s

Q: A 2.0-kg block travels around a 0.50-m radius circle with an angular speed of 12 rad/s. The circle is parallel to the xyplane and is centered on the zaxis, a distance of 0.75 m from the origin. The z component of the angular momentum around the origin is: A) 6.0 kgm2/s B) 9.0 kgm2/s C) 11 kgm2/s D) 14 kgm2/s E) 20 kgm2/s

Q: As a 2.0-kg block travels around a 0.50-m radius circle it has an angular speed of 12 rad/s. The circle is parallel to the xyplane and is centered on the zaxis, 0.75 m from the origin. The magnitude of its angular momentum around the origin is: A) 6.0 kgm2/s B) 9.0 kgm2/s C) 11 kgm2/s D) 14 kgm2/s E) 20 kgm2/s

Q: A 15-g paper clip is attached to the rim of a phonograph record with a diameter of 30 cm, spinning at 3.5 rad/s. The magnitude of its angular momentum is:A) 1.2x10-3kgm2/sB) 4.7x10-3kgm2/sC) 7.9x10-3kgm2/sD) 1.6x10-2kgm2/sE) 1.2kgm2/s

Q: Two objects are moving in the x,yplane as shown. The magnitude of their total angular momentum (about the origin O) is: A) 0kgm2/s B) 6 kgm2/s C) 12 kgm2/s D) 30 kgm2/s E) 78 kgm2/s

Q: A 2.0-kg block starts from rest on the positive xaxis 3.0 m from the origin and thereafter has an acceleration given by in m/s2. At the end of 2.0 s its angular momentum about the origin is:A) 0 kgm2/sB) (-36 kgm2/s)C) (+48 kgm2/s)D) (-96 kgm2/s)E) (+96 kgm2/s)

Q: A 6.0-kg particle moves to the right at 4.0 m/s as shown. The magnitude of its angular momentum about the point O is: A) 0kgm2/s B) 288 kgm2/s C) 144 kgm2/s D) 24 kgm2/s E) 249 kgm2/s

Q: The angular momentum vector of Earth, due to its daily rotation, is directed: A) tangent to the equator toward the east B) tangent to the equator toward the west C) north D) south E) toward the sun

Q: A particle moves along the xaxis. In order to calculate the angular momentum of the particle, you need to know: A) the size of the particle B) the rotational inertia of the particle C) the point about which the angular momentum is to be calculated D) the kinetic energy of the particle E) the acceleration of the particle

Q: Which of the following is NOT a vector? A) linear momentum B) angular momentum C) rotational inertia D) torque E) angular velocity

Q: A 2.0-kg block travels around a 0.50-m radius circle with an angular velocity of 12 rad/s. The magnitude of its angular momentum about the center of the circle is:A) 6.0 kg.m2/sB) 12 kg.m2/sC) 48 kg.m2/sD) 72 kg.m2/sE) 576 kg.m2/s

Q: The newton.second is a unit of:A) workB) angular momentumC) powerD) linear momentumE) none of these

Q: The unit kg.m2/s can be used for:A) angular momentumB) rotational kinetic energyC) rotational inertiaD) torqueE) power

Q: Possible units of angular momentum are:A) kg.m/sB) kg.m2/s2C) kg.m/s2D) kg.m2/sE) none of these

Q: The fundamental dimensions of angular momentum are:A) masslengthtime-1B) masslength-2time-2C) mass2time-1D) masslength2time-2E) none of these

Q: A single force acts on a particle situated on the positive xaxis. The torque about the origin is in the negative zdirection. The force might be: A) in the positive ydirection B) in the negative ydirection C) in the positive xdirection D) in the negative xdirection E) in the positive zdirection

Q: A force = 4.2 N + 3.7 N + 1.2 N acts on a particle located at x= 3.3 m. What is the torque on the particle around the origin?A) 14 N mB) -4.0N m + 12 N mC) 12 N mD) 14 N m"4.0 N m + 12 N mE) cannot be calculated without knowing the mass of the particle

Q: A particle is located on the xaxis at x= 2.0 m from the origin. A force of 25 N, directed 30 above the xaxis in the x-yplane, acts on the particle. What is the torque about the origin on the particle?A) 50 N m, in the positive zdirectionB) 25 N m, in the positive zdirectionC) 50 N m, in the negative zdirectionD) 25 N m, in the negative zdirectionE) There is no torque about the origin.

Q: A particle moves along the xaxis. In order to calculate the torque on the particle, you need to know: A) the velocity of the particle B) the rotational inertia of the particle C) the point about which the torque is to be calculated D) the kinetic energy of the particle E) the mass of the particle

Q: Which of the following is a vector quantity? A) angular speed B) rotational inertia C) rotational kinetic energy D) mass E) torque

Q: A yo-yo, arranged as shown, rests on a frictionless surface. When a force is applied to the string as shown, the yo-yo: A) moves to the left and rotates counterclockwise B) moves to the right and rotates counterclockwise C) moves to the left and rotates clockwise D) moves to the right and rotates clockwise E) moves to the right and does not rotate

Q: A solid sphere starts from rest and rolls down a slope that is 5.1 m long. If its speed at the bottom of the slope is 4.3 m/s, what is the angle of the slope? A) 10 B) 15 C) 20 D) 30 E) cannot be calculated without knowing the mass and radius of the sphere

Q: The coefficient of static friction between a certain cylinder and a horizontal floor is 0.40. If the rotational inertia of the cylinder about its symmetry axis is given by I= (1/2)MR2, then the maximum acceleration the cylinder can have without sliding is: A) 0.1 g B) 0.2 g C) 0.4 g D) 0.8 g E) 1.0 g

Q: A solid wheel with mass M,radius R, and rotational inertia MR2/2, rolls without sliding on a horizontal surface. A horizontal force Fis applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are: A) F= Ma, f= 0 B) F= Ma, f= Ma/2 C) F= 2Ma, f= Ma D) F= 2Ma, f= Ma/2 E) F= 3Ma/2, f= Ma/2

Q: A cylinder of radius R= 6.0 cm is on a rough horizontal surface. The coefficient of kinetic friction between the cylinder and the surface is 0.30 and the rotational inertia for rotation about the axis is given by MR2/2, where Mis its mass. Initially it is not rotating but its center of mass has a speed of 7.0 m/s. After 2.0 s the speed of its center of mass and its angular velocity about its center of mass, respectively, are: A) 1.1 m/s, 0 B) 1.1 m/s, 19 rad/s C) 1.1 m/s, 98 rad/s D) 4.7 m/s, 78 rad/s E) 5.9 m/s, 98 rad/s

Q: Two identical disks, with rotational inertia I(= 1/2 MR2), roll without slipping across a horizontal floor and then up inclines. Disk A rolls up its incline without sliding. On the other hand, disk B rolls up a frictionless incline. Otherwise the inclines are identical. Disk A reaches a height 12 cm above the floor before rolling down again. Disk B reaches a height above the floor of: A) 24 cm B) 18 cm C) 12 cm D) 8 cm E) 6 cm

Q: A hoop, a uniform disk, and a uniform sphere, all with the same mass and outer radius, start with the same speed and roll without sliding up identical inclines. Rank the objects according to how high they go, least to greatest. A) hoop, disk, sphere B) disk, hoop, sphere C) sphere, hoop, disk D) sphere, disk, hoop E) hoop, sphere, disk

Q: A hoop (I= MR2) of mass 2.0 kg and radius 0.50 m is rolling at a center-of-mass speed of 15 m/s. An external force does 750 J of work on the hoop. What is the new speed of the center of mass of the hoop? A) 19 m/s B) 22 m/s C) 24 m/s D) 27 m/s E) 68 m/s

Q: A 5.0-kg ball rolls without sliding from rest down an inclined plane. A 4.0-kg block, mounted on roller bearings totaling 100 g, rolls from rest down the same plane. At the bottom, the block has: A) greater speed than the ball B) less speed than the ball C) the same speed as the ball D) greater or less speed than the ball, depending on the angle of inclination E) greater or less speed than the ball, depending on the radius of the ball

Q: Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is: A) the one with the larger mass B) the one with the smaller mass C) the one with the larger rotational inertia D) the one with the smaller rotational inertia E) neither (they arrive together)

Q: When we apply the energy conversation principle to a cylinder rolling down an incline without sliding, we exclude the work done by friction because: A) there is no friction present B) the angular velocity of the center of mass about the point of contact is zero C) the coefficient of kinetic friction is zero D) the linear velocity of the point of contact (relative to the inclined surface) is zero E) the coefficient of static and kinetic friction are equal

Q: A hoop rolls with constant velocity and without sliding along level ground. Its rotational kinetic energy is: A) half its translational kinetic energy B) the same as its translational kinetic energy C) twice its translational kinetic energy D) four times its translational kinetic energy E) one-third its translational kinetic energy

Q: A solid sphere and a solid cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane sliding down the incline. Then: A) the sphere reaches the bottom first because it has the greater inertia B) the cylinder reaches the bottom first because it picks up more rotational energy C) the sphere reaches the bottom first because it picks up more rotational energy D) they reach the bottom together E) none of the above is true

Q: When the speed of a rear-drive car is increasing on a horizontal road the direction of the frictional force on the tires is: A) forward for all tires B) backward for all tires C) forward for the front tires and backward for the rear tires D) backward for the front tires and forward for the rear tires E) zero

Q: A forward force acting on the axle accelerates a rolling wheel on a horizontal surface. If the wheel does not slide the frictional force of the surface on the wheel is: A) zero B) in the forward direction and does zero work on the wheel C) in the forward direction and does positive work on the wheel D) in the backward direction and does zero work on the wheel E) in the backward direction and does positive work on the wheel

Q: A thin-walled hollow tube rolls without sliding along the floor. The ratio of its translational kinetic energy to its rotational kinetic energy (about an axis through its center of mass) is: A) 1 B) 2 C) 3 D) 1/2 E) 1/3

Q: Two wheels roll side-by-side without sliding, at the same speed. The radius of wheel 2 is twice the radius of wheel 1. The angular velocity of wheel 2 is: A) twice the angular velocity of wheel 1 B) the same as the angular velocity of wheel 1 C) half the angular velocity of wheel 1 D) more than twice the angular velocity of wheel 1 E) less than half the angular velocity of wheel 1

Q: A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from rest, the wheel moves with constant angular acceleration 6 rad/s2. The distance in traveled by the center of the wheel from t= 0 to t= 3 s is: A) 0 m B) 27 m C) 13.5 m D) 18 m E) none of these

Q: A wheel rolls without slipping along a horizontal road as shown. The velocity of the center of the wheel is represented by . Point P is painted on the rim of the wheel. The direction of the instantaneous velocity of point P is:

Q: When a wheel rolls without slipping, A) its motion is purely translational. B) its motion is purely rotational. C) whether its motion is purely rotational or purely translational depends on whether it is rolling up or downhill. D) its motion is a combination of rotational and translational motion. E) every point on its rim has the same linear velocity.

Q: A torque of 470 Nmacts on a flywheel. At the instant that the flywheel's angular speed is 56 rad/s, at what rate is work being done by the torque? A) 8.4 W B) 26 W C) 112 W D) 4200 W E) 2.6 x 104W

Q: A constant torque of 260 Nmacts on a flywheel. If the flywheel makes 25 complete revolutions in 2 minutes, what is the power exerted by the torque? A) 54 W B) 200 W C) 340 W D) 3.3 x 103W E) 2.0 x 104W

Q: A constant torque of 260 Nmacts on a flywheel. If the flywheel makes 25 complete revolutions, how much work has been done by the torque on the flywheel? A) 1.7 J B) 41 J C) 600 J D) 6.5 x 103J E) 4.1 x 104J

Q: A torque of 170 Nm does 4700 J of work on a rotating flywheel. If the flywheel's initial kinetic energy is 1500 J, what is its final kinetic energy? A) 1500 J B) 3200 J C) 4700 J D) 6200 J E) cannot be calculated without knowing the rotational inertia of the flywheel

Q: A disk starts from rest and rotates about a fixed axis, subject to a constant net torque. The work done by the torque during the second revolution is ______ as the work done during the first revolution. A) the same B) twice as much C) half as much D) four times as much E) one fourth as much

Q: A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The work done by the torque during the second 5 s is ______ as the work done during the first 5 s. A) the same B) half as much C) twice as much D) three times as much E) four times as much

Q: A disk has a rotational inertia of 6.0 kgm2and a constant angular acceleration of 2.0 rad/s2. If it starts from rest the work done during the first 5.0 s by the net torque acting on it is: A) 0 J B) 30 J C) 60 J D) 300 J E) 600 J

Q: A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80 Nm on the saw blade. If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 min is: A) 0 J B) 480 J C) 960 J D) 1500 J E) 1800 J

Q: A disk with a rotational inertia of 5.0 kgm2and a radius of 0.25 m rotates on a fixed axis perpendicular to the disk and through its center. A force of 2.0 N is applied tangentially to the rim. As the disk turns through half a revolution the work done by the force is: A) 1.6 J B) 2.5 J C) 6.3 J D) 10 J E) 40 J

Q: A block is attached to each end of a rope that passes over a pulley suspended from the ceiling. The blocks do not have the same mass. If the rope does not slip on the pulley, then at any instant after the blocks start moving, the rope: A) pulls on both blocks, but exerts a greater force on the heavier block B) pulls on both blocks, but exerts a greater force on the lighter block C) pulls on both blocks and exerts the same magnitude force on both blocks D) does not pull on either block E) pulls only on the lighter block

Q: A small disk of radius R1is fastened coaxially to a larger disk of radius R2. The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead view below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force as shown. The tension in the string pulling the block is:A) R1F/R2B) mR1R2F/(I- mR22)C) mR1R2F/(I+ mR22)D) mR1R2F/(I- mR1R2)E) mR1R2F/(I+ mR1R2)

Q: A small disk of radius R1is mounted coaxially with a larger disk of radius R2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless table top,as shown in the overhead view below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force as shown. The acceleration of the block is:A) R1F/mR2B) R1R2F/(I- mR22)C) R1R2F/(I+ mR22)D) R1R2F/(I- mR1R2)E) R1R2F/(I+ mR1R2)

Q: A 0.70-kg disk with a rotational inertia given by MR2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip then as the mass falls and the cylinder rotates the suspension holding the cylinder pulls up on the mass with a force of: A) 6.9 N B) 9.8 N C) 16 N D) 26 N E) 29 N