Q&A Hero

Q: A 16 kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter 0.40 m and hangs vertically, as shown. The rotational inertia of the flywheel is 0.50 kgm2. When the block is released and the cord unwinds, the acceleration of the block is: A) 0.15 g B) 0.56 g C) 0.84 g D) 1.0 g E) 1.3 g

Q: An 8.0-cm radius disk with a rotational inertia of 0.12 kgm2is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by using a crank to apply a 9.0-N.m torque to the disk. The acceleration of the mass is:A) 0.50 m/s2B) 3.9 m/s2C) 6.0 m/s2D) 12 m/s2E) 20 m/s2

Q: A certain wheel has a rotational inertia of 12 kgm2. As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s. If the net torque is constant its value is: A) 0.015Nm B) 0.18 Nm C) 0.57 Nm D) 2.1 Nm E) 13Nm

Q: A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s2. The net torque acting on it is: A) 7.0 Nm B) 14Nm C) 28Nm D) 44Nm E) none of these

Q: A disk with a rotational inertia of 5.0 kg .m2and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied tangentially to the rim. If the disk starts at rest, then after it has turned through half a revolution its angular velocity is:A) 0.57 rad/sB) 0.64 rad/sC) 0.80 rad/sD) 1.6 rad/sE) 3.2 rad/s

Q: A disk with a rotational inertia of 5.0 kgm2and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied along the rotation axis. The angular acceleration of the disk is: A) 0 rad/s2 B) 0.40 rad/s2 C) 0.60 rad/s2 D) 1.0 rad/s2 E) 2.5 rad/s2

Q: A disk with a rotational inertia of 2.0 kg.m2and a radius of 0.40 m rotates on a frictionless fixed axis perpendicular to the disk faces and through its center. A force of 5.0 N is applied tangentially to the rim. The angular acceleration of the disk is:A) 0.40 rad/s2B) 0.60 rad/s2C) 1.0 rad/s2D) 2.5 rad/s2E) 10 rad/s2

Q: A cylinder is 0.10 m in radius and 0.20 m in length. Its rotational inertia, about the cylinder axis on which it is mounted, is 0.020 kg .m2. A string is wound around the cylinder and pulled with a force of 1.0 N. The angular acceleration of the cylinder is:A) 2.5 rad/s2B) 5.0 rad/s2C) 10 rad/s2D) 15 rad/s2E) 20 rad/s2

Q: A uniform disk, a thin hoop, and a uniform solid 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 velocities after a given time t, least to greatest. A) disk, hoop, sphere B) disk, sphere, hoop C) hoop, sphere, disk D) hoop, disk, sphere E) sphere, disk, hoop

Q: = I for an object rotating about a fixed axis, where is the net torque acting on it, Iis its rotational inertia, and is its angular acceleration. This expression:A) is the definition of torqueB) is the definition of rotational inertiaC) is the definition of angular accelerationD) follows directly from Newton's second lawE) depends on a principle of physics that is unrelated to Newton's second law

Q: A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A horizontal force is applied perpendicularly to the end of the stick at 0 cm, as shown. A second horizontal force (not shown) is applied at the 100-cm end of the stick. If the stick does not rotate: A) for all orientations of B) for all orientations of C) for all orientations of D) for some orientations of and for others E) for some orientations of and for others

Q: A rod is pivoted about its center. A 5-N force is applied 4 m from the pivot and another 5-N force is applied 2 m from the pivot, as shown. The magnitude of the total torque about the pivot is:A) 0 N.mB) 5.0N.mC) 8.7 N.mD) 15 N.mE) 26 N.m

Q: The figure shows forces acting on a meter stick, which is constrained to rotate around the axis indicated by the dot ï‚·ï€®ï€ Which force(s) create a positive torque around that axis? A) only B) and C) only D) ,and E) only

Q: A force is applied to a billiard ball. In order to calculate the torque created by the force, you also need to know: A) the mass of the ball B) the rotational inertia of the ball C) the kinetic energy of the ball D) the angular speed of the ball E) the location and orientation of the axis of rotation of the ball

Q: A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applied. Of the following alternatives the greatest angular acceleration is obtained if the force is: A) applied tangentially halfway between the axis and the rim B) applied tangentially at the rim C) applied radially halfway between the axis and the rim D) applied radially at the rim E) applied at the rim but neither radially nor tangentially

Q: The meter stick shown below rotates about an axis through the point marked ., 20 cm from one end. Five forces act on the stick: one at each end, one at the pivot point, and two 40 cm from one end, as shown. The magnitudes of the forces are all the same. Rank the forces according to the magnitudes of the torques they produce about the pivot point, least to greatest.A) , , , , B) and tie, then , , C) and tie, then , , D) , , , and tie, then E) and tie, then , then and tie

Q: A force with a given magnitude is to be applied to a wheel. The torque can be maximized by: A) applying the force near the axle, radially outward from the axle B) applying the force near the rim, radially outward from the axle C) applying the force near the axle, parallel to a tangent to the wheel D) applying the force at the rim, tangent to the rim E) applying the force at the rim, at 45ï‚°to the tangent

Q: The torque exerted on an object can be written as. Here,: A) is the radius of the object. B) is a vector pointing from the axis of rotation to the point where the force is applied. C) is always perpendicular to. D) is a vector pointing from the point where the force is applied to the axis of rotation. E) points along the axis of rotation.

Q: A solid uniform sphere of radius Rand mass Mhas a rotational inertia about a diameter that is given by (2/5)MR2. A light string of length 2.5 Ris attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is: A) (2/5)MR2 B) 9MR2 C) 16MR2 D) 47/5MR2 E) (82/5)MR2

Q: The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, where Mis its mass and Ris its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is: A) MR2 B) (2/5)MR2 C) (3/5)MR2 D) (5/2)MR2 E) (7/5)MR2

Q: When a thin uniform stick of mass Mand length Lis pivoted about its midpoint, its rotational inertia is ML2/12. When pivoted about a parallel axis through one end, its rotational inertia is: A) ML2/12 B) ML2/6 C) ML2/3 D) 7ML2/12 E) 13ML2/12

Q: A thin rod of length Lhas a density that increases along its length, = 0x. What is the rotational inertia of the rod around its less dense end?A) ML2/12B) ML2/6C) ML2/3D) ML2/2E) ML2

Q: The rotational inertia of a disk about its axis is 0.70 kg.m2. When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes:A) 0.32 kg.m2B) 0.54 kg.m2C) 0.70 kg.m2D) 0.86 kg.m2E) 1.0 kg.m2

Q: To increase the rotational inertia of a solid disk about its axis without changing its mass: A) drill holes near the rim and put the material near the axis B) drill holes near the axis and put the material near the rim C) drill holes at points on a circle near the rim and put the material at points between the holes D) drill holes at points on a circle near the axis and put the material at points between the holes E) do none of the above (the rotational inertia cannot be changed without changing the mass)

Q: A uniform solid cylinder made of lead has the same mass and the same length as a uniform solid cylinder made of wood. The rotational inertia of the lead cylinder compared to the wooden one is: A) greater B) less C) same D) unknown unless the radii are given E) unknown unless both the masses and the radii are given

Q: Two uniform circular disks having the same mass and the same thickness are made from different materials. The disk with the smaller rotational inertia is: A) the one made from the more dense material B) the one made from the less dense material C) neither both rotational inertias are the same D) the disk with the larger angular velocity E) the disk with the larger torque

Q: A and B are two solid cylinders made of aluminum. Their dimensions are shown. The ratio of the rotational inertia of B to that of A about the common axis X-X' is:A) 2B) 4C) 8D) 16E) 32

Q: Consider four objects, each having the same mass and the same radius: 1) a solid sphere 2) a hollow sphere 3) a flat disk in the x,yplane 4) a hoop in the x,yplane The order of increasing rotational inertia about an axis through the center of mass and parallel to the zaxis is: A) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 1, 3, 2, 4 D) 4, 2, 3, 1 E) 3, 1, 2, 4

Q: The rotational inertia of a wheel about its axle does not depend upon its: A) diameter B) mass C) distribution of mass D) speed of rotation E) material composition

Q: The rotational inertia of a thin cylindrical shell of mass M, radius R, and length Labout its central axis (X - X') is: A) MR2/2 B) ML2/2 C) ML2 D) MR2 E) none of these

Q: A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 x10-3kgm2is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. At any instant after the blocks start moving the object with the greatest kinetic energy is:A) the heavier blockB) the lighter blockC) the pulleyD) either block (the two blocks have the same kinetic energy)E) none (all three objects have the same kinetic energy)

Q: A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 x10-3kgm2is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. When the velocity of the heavier block is 2.0 m/s the total kinetic energy of the pulley and blocks is:A) 2.0 JB) 12 JC) 14 JD) 22 JE) 28 J

Q: Three balls, with masses of 3M, 2M,and M,are fastened to a massless rod of length Las shown. The rotational inertia about the left end of the rod is: A) ML2/2 B) ML2 C) 3ML2/2 D) 6ML2 E) 3ML2

Q: Four identical particles, each with mass m, are arranged in the x, yplane as shown. They are connected by light sticks to form a rigid body. If m= 2.0 kg and a= 1.0 m, the rotational inertia of this array about the y-axis is: A) 4.0 kgm2 B) 12 kgm2 C) 9.6 kgm2 D) 4.8 kgm2 E) none of these

Q: Three identical balls are tied by light strings to the same rod and rotate around it, as shown below. Rank the balls according to their rotational inertia, least to greatest. A) 1, 2, 3 B) 3, 2, 1 C) 3, then 1 and 2 tie D) 1, 3, 2 E) All are the same

Q: A wheel starts from rest and spins with a constant angular acceleration. As time goes on the acceleration vector for a point on the rim: A) decreases in magnitude and becomes more nearly tangent to the rim B) decreases in magnitude and becomes more nearly radial C) increases in magnitude and becomes more nearly tangent to the rim D) increases in magnitude and becomes more nearly radial E) increases in magnitude but retains the same angle with the tangent to the rim

Q: The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if: A) the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 4 B) the magnitude of the angular velocity is multiplied by a factor of 4 and the angular acceleration is not changed C) the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 2 D) the magnitude of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed E) the magnitude of the angular velocity is multiplied by a factor of 2 and the magnitude of the angular acceleration is multiplied by a factor of 4

Q: Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the magnitude of the radial acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is: A) 1 B) 2 C) 1/2 D) 4 E) 1/4

Q: For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim is: A) 1 B) 2 C) 1/2 D) 4 E) 1/4

Q: For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is: A) 1 B) 2 C) 1/2 D) 4 E) 1/4

Q: For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed of a point halfway between the center and the rim is: A) 1 B) 2 C) 1/2 D) 4 E) 1/4

Q: A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s2. The tangential acceleration of a point on its rim is: A) 5.0 rad/s2 B) 3.0 m/s2 C) 5.0 m/s2 D) 6.0 m/s2 E) 12 m/s2

Q: String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, the segment's acceleration changes by: A) 0 m/s2 B) 0.010 m/s2 C) 0.020 m/s2 D) 0.10 m/s2 E) 0.20 m/s2

Q: Wrapping paper is being unwrapped from a 5.0-cm radius tube, free to rotate on its axis. If it is pulled at the constant rate of 10 cm/s and does not slip on the tube, the angular velocity of the tube is: A) 2.0 rad/s B) 5.0 rad/s C) 10 rad/s D) 25 rad/s E) 50 rad/s

Q: A car travels north at constant velocity. It goes over a piece of mud which sticks to the tire. The initial acceleration of the mud, as it leaves the ground, is: A) vertically upward B) horizontally to the north C) horizontally to the south D) zero E) upward and forward at 45ï‚°to the horizontal

Q: A particle moves in a circular path of radius 0.10 m with a constant angular speed of 5 rev/s. The acceleration of the particle is:A) 0.10m/s2B) 0.50 m/s2C) 500m/s2D) 2.5 m/s2E) 102m/s2

Q: The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point P is:A) 7.0 m/sB) 14rad/sC) 7rad/sD) 0.70 m/sE) none of these

Q: A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s2. The cord will unwind in: A) 0.82 s B) 2.0 s C) 12 s D) 16 s E) 130 s

Q: A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. The time it takes to make 10 revolutions is: A) 0.50 s B) 0.71 s C) 2.2 s D) 2.8 s E) 5.6 s

Q: A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. When it has made 10 rev its angular velocity is: A) 8.9 rad/s B) 16 rad/s C) 22 rad/s D) 32 rad/s E) 250 rad/s

Q: A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s2. By the time it stops it will have turned through: A) 81 rad B) 160 rad C) 245 rad D) 330 rad E) 410 rad

Q: A wheel rotates with a constant angular acceleration of rad/s2. During a certain time intervalits angular displacement is rad. At the end of the interval its angular velocity is 2rad/s. Its angular velocity at the beginning of the interval is:A) 0 rad/sB) 1 rad/sC)rad/sD) rad/sE) 2rad/s

Q: A flywheel is initially rotating at 20 rad/s and has a constant angular acceleration. After 9.0 s it has rotated through 450 rad. Its angular acceleration is: A) 3.3 rad/s B) 4.4 rad/s C) 6.7 rad/s D) 11 rad/s E) 48 rad/s

Q: A wheel starts from rest and has an angular acceleration that is given by (t) = (6.0 rad/s4)t2. The time it takes to make 10 rev is:A) 1.3 sB) 2.1 sC) 2.8 sD) 3.3 sE) 4.0 s

Q: A wheel starts from rest and has an angular acceleration that is given by (t) = 6 rad/s4)t2. The angle through which it turns in time tis given by:A) [(1/8)t4] rad/s4B) [(1/4)t4] rad/s4C) [(1/2)t4] rad/s4D) (t4) rad/s4E) 12 rad

Q: A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s4)t2.It stops in a time of: A) 1.7 s B) 2.6 s C) 3.0 s D) 4.4 s E) 9.0 s

Q: A wheel starts from rest and has an angular acceleration that is given by (t) = (6.0 rad/s4)t2. After it has turned through 10 rev its angular velocity is:A) 63 rad/sB) 75 rad/sC) 89 rad/sD) 130 rad/sE) 210 rad/s

Q: This graph shows the angular velocity of a turntable as a function of time. What is its average angular acceleration between t = 2 s and t = 4 s?A) -10 rad/s2B) -5 rad/s2C) 0 rad/s2D) 5 rad/s2E) 10 rad/s2

Q: This graph shows the angular velocity of a turntable as a function of time. What is its angular acceleration at t = 3.5 s?A) -10 rad/s2B) -5 rad/s2C) 0 rad/s2D) 5 rad/s2E) 10 rad/s2

Q: The angular velocity of a rotating turntable is given in rad/s by (t) = 4.5 + 0.64t- 2.7t2. What is its average angular acceleration between t= 1.0 s and t= 3.0 s?A) 0.64 rad/s2B) -5.4 rad/s2C) -7.7 rad/s2D) -10 rad/s2E) -27 rad/s2

Q: The angular velocity of a rotating turntable is given in rad/s by (t) = 4.5 + 0.64t- 2.7t2. What is its angular acceleration at t = 2.0 s?A) -10 rad/s2B) -5.0 rad/s2C) -5.4 rad/s2D) 2.4 rad/s2E) 3.1 rad/s2

Q: Instantaneous angular speed is: A) total angular displacement divided by time B) the integral of the displacement over time C) the rate at which the angular acceleration is changing D) the magnitude of the instantaneous angular velocity E) a vector directed along the axis of rotation

Q: This graph shows the angular position of an object as a function of time. What is its instantaneous angular velocity at t= 1.5 s?A) -6 rad/sB) 6 rad/sC) 9 rad/sD) 12rad/sE) Need additional information.

Q: This graph shows the angular position of an object as a function of time. What is its average angular velocity between t= 5 s and t= 9 s?A) 3 rad/sB) -3 rad/sC) 12 rad/sD) -12 rad/sE) Need additional information.

Q: The coordinate of an object is given as a function of time by = 7t- 3t2, where is in radians and tis in seconds. Its angular velocity at t= 3 s is:A) -11 rad/sB) -3.7 rad/sC) 1.0 rad/sD) 3.7 rad/sE) 11 rad/s

Q: The coordinate of an object is given as a function of time by = 7t- 3t2, where is in radians and t is in seconds. Its average velocity over the interval from t= 0 to t= 2 s is:A) 5 rad/sB) -5 rad/sC) 11 rad/sD) -11 rad/sE) 1 rad/s

Q: An object rotates from 1to 2through an angle that is less than π radians. Which of the following results in a positive angular displacement?A) 1 = 45, 2= -45B) 1 = 45, 2= 15C) 1 = 45, 2= -45D) 1 = 135, 2= -135E) 1 = -135, 2= 135

Q: The fan shown has been turned on and is slowing as it rotates clockwise. The direction of the acceleration of the point X on the fan tip could be:A) B) C) D) E) ->

Q: A wheel initially has an angular velocity of -36 rad/s but after 6.0 s its angular velocity is -24 rad/s. If its angular acceleration is constant the value is:A) 2.0 rad/s2B) -2.0 rad/s2C) 3.0 rad/s2D) -3.0 rad/s2E) -6.0 rad/s2

Q: A wheel initially has an angular velocity of 36 rad/s but after 6.0s its angular velocity is 24 rad/s. If its angular acceleration is constant the value is:A) 2.0 rad/s2B) -2.0 rad/s2C) 3.0 rad/s2D) -3.0 rad/s2E) 6.0 rad/s2

Q: A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s2 and is slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial angular velocity? A) 3.0 s B) 6.0 s C) 9.0 s D) 18 s E) 36 s

Q: The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration of this wheel is:A) 42rad/s2B) 2rad/s2C) 1/30 rad/s2D) 2/30 rad/s2E) 4rad/s2

Q: The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then: A) the body is slowing down B) the body is speeding up C) the body is starting to turn in the opposite direction D) the axis of rotation is changing orientation E) none of the above

Q: If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning: A) clockwise about an axis that is perpendicular to the page B) counterclockwise about an axis that is perpendicular to the page C) about an axis that is parallel to the page D) about an axis that is changing orientation E) about an axis that is getting longer

Q: A phonograph turntable, initially rotating at 0.75 rev/s, slows down and stops in 30 s. The magnitude of its average angular acceleration for this process is:A) 1.5 rad/s2B) 1.5rad/s2C) /40 rad/s2D) /20 rad/s2E) 0.75 rad/s2

Q: A flywheel rotating at 12 rev/s is brought to rest in 6 s. The magnitude of the average angular acceleration of the wheel during this process is:A) 1/rad/s2B) 2 rad/s2C) 4 rad/s2D) 4rad/s2E) 72 rad/s2

Q: Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min. Its average angular acceleration is: A) 3.14 rad/s2 B) 30 rad/s2 C) 30 rev/s2 D) 50 rev/min2 E) 1800 rev/s2

Q: A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter 40 m. The total angle through which she revolves is: A) 50 rad B) 75 rad C) 150 rad D) 314 rad E) none of these

Q: The angular speed of the minute hand of a watch is:A) (60/) rad/sB) (1800/) rad/sC) () rad/sD) (/1800) rad/sE) (/60) rad/s

Q: The angular speed of the second hand of a watch is:A) (/1800) rad/sB) (/60) rad/sC) (/30) rad/sD) (2 ) rad/sE) (60) rad/s