Exam 10: Dynamics of Rotational Motion

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).You release the hanging blocks simultaneously from rest,and call t_L the time taken by the block on the left and t_R the time taken by the block on the right to reach the bottom,respectively.The bar,pulley,and rope have negligible mass,the rope does not slip,and there is no friction in the axle of the pulley.Under these conditions

The angular momentum of a system remains constant

A torque of 12 N • m is applied to a solid,uniform disk of radius 0.50 m,causing the disk to accelerate at What is the mass of the disk?

A 1.10-kg wrench is acting on a nut trying to turn it.The length of the wrench lies directly to the east of the nut.A force 150.0 N acts on the wrench at a position 15.0 cm from the center of the nut in a direction 30.0° north of east.What is the magnitude of the torque about the center of the nut?

A record is dropped vertically onto a freely rotating (undriven)turntable.Frictional forces act to bring the record and turntable to a common angular speed.If the rotational inertia of the record is 0.54 times that of the turntable,what percentage of the initial kinetic energy is lost?

A wheel has a radius of 0.40 m and is mounted on frictionless bearings.A block is suspended from a rope that is wound on the wheel and attached to it (see figure).The wheel is released from rest and the block descends 1.5 m in 2.00 s without any slipping of the rope.The tension in the rope during the descent of the block is 20 N.What is the moment of inertia of the wheel?

For the apparatus shown in the figure,there is no slipping between the cord and the surface of the pulley.The blocks have mass of 3.0 kg and 5.7 kg,and the pulley has a radius of and a mass of 10.3 kg.At the instant the 5.7 kg mass has fallen 1.5 m starting from rest,find the speed of each block.(Assume the pulley is in the shape of a uniform solid disk and has no friction in its axle.)

In the figure,a very light rope is wrapped around a wheel of radius R = 2.0 meters and does not slip.The wheel is mounted with frictionless bearings on an axle through its center.A block of mass 14 kg is suspended from the end of the rope.When the system is released from rest it is observed that the block descends 10 meters in 2.0 seconds.What is the moment of inertia of the wheel?

A lawn roller in the form of a uniform solid cylinder is being pulled horizontally by a horizontal force B applied to an axle through the center of the roller,as shown in the figure.The roller has radius 0.65 meters and mass 51 kg and rolls without slipping.What magnitude of the force B is required to give the center of mass of the roller an acceleration of ?

In an experiment,a student brings up the rotational speed of a piece of laboratory apparatus to 30.0 rpm.She then allows the apparatus to slow down uniformly on its own,and counts 240 revolutions before the apparatus comes to a stop.The moment of inertia of the apparatus is known to be 0.0850 kg • m².What is the magnitude of the retarding torque on the apparatus?

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg • m² is rotating freely with an angular speed of 1.0 rad/s.Two people,each having a mass of 60 kg,are standing right outside the edge of the merry-go-round and step on it with negligible speed.What is the angular speed of the merry-go-round right after the two people have stepped on?

61)A bicycle wheel of radius 0.36 m and mass 3.2 kg is set spinning at 4.00 rev/s.A very light bolt is attached to extend the axle in length,and a string is attached to the axle at a distance of 0.10 m from the wheel.Initially the axle of the spinning wheel is horizontal,and the wheel is suspended only from the string.We can ignore the mass of the axle and spokes.At what rate will the wheel process about the vertical?

A thin cylindrical shell is released from rest and rolls without slipping down an inclined ramp that makes an angle of 30° with the horizontal.How long does it take it to travel the first 3.1 m?

What is the torque about the origin on a particle located at = 3 m + 4 m - 2 m if a force acts on the particle?

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above the horizontal.After it has rolled 4.20 m along the ramp,what is the magnitude of the linear acceleration of its center of mass?

A potter's wheel,with rotational inertia 46 kg • m²,is spinning freely at 40 rpm.The potter drops a lump of clay onto the wheel,where it sticks a distance from the rotational axis.If the subsequent angular speed of the wheel and clay is 32 rpm what is the mass of the clay?

A ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface as shown in the figure.When the ball reaches its maximum height on the frictionless surface,it is

A very thin uniform rod,2.40 m long and of weight 135 N,has a frictionless hinge at its lower end.It starts out vertically from rest and falls,pivoting about the hinge.Just as it has rotated through an angle of 55.0°,what is the downward acceleration of the end farthest from the hinge?

A uniform disk has a mass of 3.7 kg and a radius of 0.40 m.The disk is mounted on frictionless bearings and is used as a turntable.The turntable is initially rotating at 30 rpm.A thin-walled hollow cylinder has the same mass and radius as the disk.It is released from rest,just above the turntable,and on the same vertical axis.The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable.What is the final angular momentum of the system?

A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg • m².The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings.A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of .The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure).What is the angular velocity of the turntable just after the ball is caught?