Exam 9: Rotation of Rigid Bodies

A 4.50-kg wheel that is 34.5 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s.What is the magnitude of the angular acceleration of the wheel?

A turbine blade rotates with angular velocity .What is the angular acceleration of the blade at

A 1.15-kg grinding wheel 22.0 cm in diameter is spinning counterclockwise at a rate of 20.0 revolutions per second.When the power to the grinder is turned off,the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest. (a)What was the angular acceleration (in rad/s²)of the grinding wheel as it came to rest if we take a counterclockwise rotation as positive? (b)How many revolutions did the wheel make during the time it was coming to rest?

When a 2.75-kg fan,having blades 18.5 cm long,is turned off,its angular speed decreases uniformly from 10.0 rad/s to 6.30 rad/s in 5.00 s. (a)What is the magnitude of the angular acceleration of the fan? (b)Through what angle (in degrees)does it turn while it is slowing down during the 5.00 s? (c)If its angular acceleration does not change,how long after it is turned off does it take the fan to stop.

A uniform solid sphere has a moment of inertia I about an axis tangent to its surface.What is the moment of inertia of this sphere about an axis through its center?

The angular acceleration of a wheel is given in by where t is in seconds.If the wheel starts from rest at when is the next time the wheel is at rest?

A 1.25-kg ball begins rolling from rest with constant angular acceleration down a hill.If it takes 3.60 s for it to make the first complete revolution,how long will it take to make the next complete revolution?

A 3.45-kg centrifuge takes 100 s to spin up from rest to its final angular speed with constant angular acceleration.A point located 8.00 cm from the axis of rotation of the centrifuge moves with a speed of 150 m/s when the centrifuge is at full speed. (a)What is the angular acceleration (in rad/s²)of the centrifuge as it spins up? (b)How many revolutions does the centrifuge make as it goes from rest to its final angular speed?

A uniform solid sphere of mass M and radius R rotates with an angular speed ω about an axis through its center.A uniform solid cylinder of mass M,radius R,and length 2R rotates through an axis running through the central axis of the cylinder.What must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere?

In the figure,point P is at rest when it is on the x-axis.The linear speed of point P when it reaches the y-axis is closest to

In the figure,a weightlifter's barbell consists of two identical uniform spherical masses each with radius 0.17 m and mass of 50 kg.The weights are connected by a 0.96-m uniform steel rod with a mass of 12 kg.Find the moment of inertia of the barbell about the axis through the center (see figure).

At any angular speed,a certain uniform solid sphere of diameter D has half as much rotational kinetic energy as a certain uniform thin-walled hollow sphere of the same diameter when both are spinning about an axis through their centers.If the mass of the solid sphere is M,the mass of the hollow sphere is

When you ride a bicycle,in what direction is the angular velocity of the wheels?

An extremely light rod 1.00 m long has a 2.00-kg mass attached to one end and a 3.00-kg mass attached to the other.The system rotates at a constant angular speed about a fixed axis perpendicular to the rod that passes through the rod 30.0 cm from the end with the 3.00-kg mass attached.The kinetic energy of the system is measured to be 100.0 J. (a)What is the moment of inertia of this system about the fixed axis? (b)What is the angular speed (in revolutions per second)of this system?

When a rigid body rotates about a fixed axis,all the points in the body have the same

While spinning down from 500.0 rpm to rest,a solid uniform flywheel does of work.If the radius of the disk is what is its mass?

A dumbbell-shaped object is composed by two equal masses,m,connected by a rod of negligible mass and length r.If I₁ is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I₂ is the moment of inertia with respect to an axis passing through one of the masses,it follows that

A horizontal disk rotates about a vertical axis through its center.Point P is midway between the center and the rim of the disk,and point Q is on the rim.If the disk turns with constant angular velocity,which of the following statements about it are true? (There may be more than one correct choice.)

As you are leaving a building,the door opens outward.If the hinges on the door are on your right,what is the direction of the angular velocity of the door as you open it?

In the figure,two blocks,of masses 2.00 kg and 3.00 kg,are connected by a light string that passes over a frictionless pulley of moment of inertia 0.00400 kg • m² and radius 5.00 cm.The coefficient of friction for the tabletop is 0.300.The blocks are released from rest.Using energy methods,find the speed of the upper block just as it has moved 0.600 m.