Exam 10: Rotation

A meter stick,sitting on a frictionless table top,is struck by a wad of clay with a force,F = 4.0 N at an angle of as shown.The meter stick will rotate in the plane of the table.Determine the magnitude of the torque about the axis of rotation located at the pivot point at the center of the stick.

A uniform solid cylinder,a hollow cylinder,and a uniform solid sphere are rolling at the same speed on a horizontal table without slipping.If they all have the same mass and radius,which statement is true?

A massless string is wrapped around a cylinder of mass 0.400 kg and radius 0.200 m.The string is attached to the ceiling.The cylinder is released.As it falls,the string unwinds.What is the magnitude of the angular acceleration of the cylinder as it falls in rad/s²?

A uniform solid sphere of mass M and radius R is rolling without slipping along a level plane when it encounters a ramp that is at an angle of $\theta$ = 32.0^o above horizontal.The maximum distance that the sphere rolls without slipping up the ramp before (instantaneously)stopping and rolling back down is 3.15 m.What was the linear speed of the sphere before it encountered the ramp?

A sphere rolls without slipping down an inclined plane that makes an angle 30 ^$\circ$ from the horizontal.The vertical height change is h.Which one of the following statements concerning the velocity when it reaches the bottom is true?

A bug crawls from the center to the edge of a uniform disk that is freely turning at 20 rpm.The disk has a mass of 11 grams and a radius of 26 cm.If the angular speed of the disk is 12.6 rpm when the bug reaches the disk's edge,what is the mass of the bug?

Two masses are hung by a massless cord over a disk with radius R and mass M as shown.If the angular velocity of the disk is 2 rad/s counterclockwise and is not changing,which one of the following statements is true?

What is the moment of inertia of a solid sphere of mass m and radius r about a line parallel to another line passing through the center of the sphere? The distance between the lines is half the radius of the sphere.

A rigid body of moment of inertia 0.5 kg m² rotates with constant angular velocity about a fixed axis.It has kinetic energy of 1.5 J.The magnitude of the angular momentum of the rigid body is

In first gear,a motorcycle engine produces 902 Nm of torque on the rear wheel.If the rear wheel is lifted off the road and free to spin without friction,how long will it take the engine to spin the wheel from rest to 200 revolutions per minute (corresponding to the outer part of the wheel moving at approximately 24 km/h)if the wheel were on the road? Treat the rear wheel as a hollow cylinder with inner diameter 50 cm and outer diameter 64 cm,with a mass of 13 kg.

An object made of two disc shaped sections A and B,as shown in the figure is rotating about an axis through the center of disc A)The masses and the radii of discs A and B are respectively 2 kg and 0.2 kg,and 25 cm and 2.5 cm.If the axial frictional torque is 0.2 Nm,how long will it take for the object to come to a stop if it is rotating with an angular velocity of -2 $\pi$ rad/s?

A bowling ball,which can be treated as a solid sphere with a diameter of 21.6 cm and a weight of 33 kg,rolls down a bowling lane at a speed of 21 km/h.The kinetic energy of the bowling ball is

Three objects,a hoop,a disk,and a solid sphere start from the top of a hill and roll without slipping down to the bottom.Which one of the following statements is true?

A massless string is wrapped around a cylinder of mass 4.00 kg and radius 0.100 m.A force of 100 N acts on the string.How long in seconds does it take to reach an angular speed of 100 radians/s starting from rest?

A boy of mass 55 kg runs on a line tangent to the edge of a merry-go-round,whose mass is 125 kg and radius 1.2 m.He jumps onto the merry-go-round,and the angular speed of the merry-go-round becomes 2.2 radians per second.How fast was the boy running before he landed on the merry-go-round?

A solid ball of mass 2 kg and diameter 20 cm is rotating about its diameter at 100 rev/min.The kinetic energy of rotation is

Two solid steel balls,one small and one large,are on an incline plane.The large ball has a diameter of 3.0 cm and the small ball has a diameter of 1.0 cm.Starting from rest,the two balls roll without slipping down the incline plane until their centers of mass are 1 m below their starting positions.If it takes the large ball 2.0 seconds to roll down the inclined plane,how long will it take the small ball to roll down the inclined plane?

The tangential force F shown in figure below is applied to a disc is allowed to rotate about an axis through its center.The diameter of the disc is 24.0 cm.The magnitude of this tangential force is given in the graph of F vs.Angular Position.With the disc at rest initially and ignoring frictional torque,the disc's angular velocity after one full rotation is -31.4 rad/sec.What is the moment of inertia of the disk?

A baton consists of a nearly massless rod of length L and two spheres attached to the ends of the rod,whose masses are each M and whose centers are separated by L.The spheres have radius R.If the sphere radius R is not negligible compared to the length L,what is the moment of inertia of the baton about an axis perpendicular to its length and passing through its center?

If ,then