Exam 10: Rotational Motion

A puck on a frictionless air hockey table has a mass of 5.0 g and is attached to a cord passing through a hole in the surface as in the figure.The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s.The cord is then pulled from below,shortening the radius to 1.0 m.The new angular velocity (in rad/s)is

A solid sphere (radius R,mass M)rolls without slipping down an incline as shown in the figure.The linear acceleration of its center of mass is

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 8 minutes?

A uniform rod of mass M = 1.2 kg and length L = 0.80 m,lying on a frictionless horizontal plane,is free to pivot about a vertical axis through one end,as shown.The moment of inertia of the rod about this axis is given by (1/3)ML².If a force (F = 5.0 N, $\theta$ = 40 $\degree$ )acts as shown,what is the resulting angular acceleration about the pivot point?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?

A thin rod of mass M and length L is struck at one end by a ball of clay of mass m,moving with speed v as shown in the figure.The ball sticks to the rod.After the collision,the angular momentum of the clay-rod system about A,the midpoint of the rod,is

Stars originate as large bodies of slowly rotating gas.Because of gravity,these clumps of gas slowly decrease in size.The angular velocity of a star increases as it shrinks because of

Particles (mass of each = 0.40 kg)are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass.This rigid body is free to rotate about a frictionless pivot at the 0-cm end.The body is released from rest in the horizontal position.What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot?

The graphs below show angular velocity as a function of time.In which one is the magnitude of the angular acceleration constantly decreasing?

The net work done in accelerating a propeller from rest to an angular velocity of 200 rad/s is 3 000 J.What is the moment of inertia of the propeller?

When an object is effectively isolated from external torques,like an ice skater twirling on the tip of one skate,the angular momentum of the object

A regulation basketball has a 25.0-cm diameter and a mass of 0.560 kg.It may be approximated as a thin spherical shell with a moment of inertia $\frac { 2 } { 3 }$ MR².Starting from rest,how long will it take a basketball to roll without slipping 4.00 m down an incline at 30.0 $\degree$ to the horizontal?

A particle whose mass is 2.0 kg moves in the xy plane with a constant speed of 3.0 m/s along the direction $\hat { \mathbf { r } } = \hat { \mathbf { i } } + \hat { j }$ .What is its angular momentum (in kg.m²/s)relative to the point (0,5.0)meters?

A solid sphere,spherical shell,solid cylinder and a cylindrical shell all have the same mass m and radius R.If they are all released from rest at the same elevation and roll without slipping,which reaches the bottom of an inclined plane first?

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?

Two vectors lying in the xy plane are given by the equations $\overrightarrow { \mathbf { A } } = 5 \hat { \mathbf { i } } + 2 \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { B } } = 2 \hat { \mathbf { i } } - 3 \hat { \mathbf { j } }$ .The value of $\overrightarrow { \mathbf { A } } \times \overrightarrow { \mathbf { B } }$ is

A solid sphere,a solid cylinder,a spherical shell,and a hoop all have the same mass and radius.Each are rolling on a horizontal surface with the same center of mass speed,and then they roll up identical inclines.Which one goes the greatest distance up its incline?

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.Relative to the positive direction of the axis of rotation,the angular positions of the sphere are negative,its angular velocity is negative,and its angular acceleration is positive.The sphere is

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity increases to 40 rad/s.Assume that the angular acceleration was constant during the 5.0-s interval.How many revolutions does the wheel turn through during the 5.0-s interval?

The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper.If M = 2.0 kg and L = 80 cm,what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles.