Exam 10: Dynamics of Rotational Motion

A uniform solid 5.25-kg cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal.How fast is it moving after it has rolled down the plane?

A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center.Starting with an angular velocity of 2.40 rev/s,it stops after turning through 18.2 rev with uniform acceleration.The net torque acting on this sphere as it is slowing down is closest to

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of .If the arms are pulled in so the moment of inertia decreases to ,what is the final angular speed?

In the figure,the rotor of a gyroscope is a uniform disk that has a radius of 13.8 cm and a moment of inertia about its axis of .The length of the rotor shaft is 6.9 cm.The ball pivot at P is frictionless.At a given instant,the rotor shaft is horizontal and the rotor is rotating with an angular velocity of 90 rad/s about its axis OP,as shown.The rotor is viewed from point Q on the axis.The precessional linear velocity of point O,including the direction seen from point Q,is closest to

Consider a uniform solid sphere of radius R and mass M rolling without slipping.Which form of its kinetic energy is larger,translational or rotational?

A 95 N force exerted at the end of a torque wrench gives rise to a torque of What is the angle (assumed to be less than 90°)between the wrench handle and the direction of the applied force?

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii and are of uniform density.If the three are released simultaneously at the top of an inclined plane and roll without slipping,which one will reach the bottom first?

A uniform solid sphere is rolling without slipping along a horizontal surface with a speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal.What is the speed of the sphere after it has rolled 3.00 m up the ramp,measured along the surface of the ramp?

A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm rolls without slipping up a ramp that rises at 30.0° above the horizontal.The speed of the ball at the base of the ramp is 2.63 m/s.While the ball is moving up the ramp,find (a)the acceleration (magnitude and direction)of its center of mass and (b)the friction force (magnitude and direction)acting on it due to the surface of the ramp.