Exam 9: Rotational Motion

A wheel starts from rest and has a uniform angular acceleration of 4.0 rad/s².After the wheel completes its first revolution,how long does it take for it to make its second complete revolution?

A string is wrapped tightly around a fixed frictionless pulley that has a moment of inertia of 0.0352 kg ∙ m² and a radius of 12.5 cm.The string is pulled away from the pulley exerting a constant force of 5.00 N on the pullley causing the pulley to rotate.What is the speed of the string after it has unwound 1.25 m if the string does not slip on the pulley?

A turntable 45 cm in diameter starts from rest and makes its first complete revolution in 3.4 s with constant angular acceleration.If it maintains the same acceleration,how long will it take the turntable to make its second complete revolution?

A particular motor can provide a maximum torque of 110 N ∙ m.Assuming that all of this torque is used to accelerate a solid,uniform,cylindrical flywheel of mass 10.0 kg and radius 3.00 m,how long will it take for the flywheel to accelerate from rest to $8.13 \mathrm { rad } / \mathrm { s } ?$

A bicycle wheel has an initial angular speed of 7.2 rad/s.After turning through $\text { one-half }$ of a revolution,the angular speed is reduced to 2.2 rad/s.If the angular acceleration of the wheel was constant during the motion,how long will it take the wheel to make the $\text { one-half }$ revolution?

As shown in the figure,a 35.30-kg box is attached to a light string that is wrapped around a cylindrical frictionless spool of radius 10.0 cm and moment of inertia 4.00 kg ∙ m².The spool is suspended from the ceiling,and the box is then released from rest a distance 3.50 m above the floor.How long does it take for the box to reach the floor?

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O,as shown in the cross-sectional view in the figure.A rope wrapped around the outer radius R₁ = 1.0 m exerts a force of magnitude F₁ = 5.0 N to the right.A second rope wrapped around another section of radius R₂ = 0.50 m exerts a force of magnitude F₂ = 6.0 N downward.What is the angular acceleration of the cylinder?

To drive a typical car at 40 mph on a level road for one hour requires about 3.2 × 10⁷ J of energy.Suppose we tried to store this much energy in a spinning,solid,uniform,cylindrical flywheel.A large flywheel cannot be spun too fast or it will fracture.If we used a flywheel of diameter 1.2 m and mass 400 kg,what angular speed would be required to store 3.2 × 10⁷ J?

The rotating systems shown in the figure differ only in that the two identical movable blocks are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).If 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,then

The drive chain in a bicycle is exerting a torque of 0.850 N ∙ m to the wheel of the bicycle.You can treat the wheel as a thin uniform hoop (or ring)with a mass of 0.750 kg and a radius of 33.0 cm.What is the angular acceleration of the wheel?

Two uniform solid balls,one of radius R and mass M,the other of radius 2R and mass 8M,roll down a high incline.They start together from rest at the top of the incline.Which one will reach the bottom of the incline first?

A cinder block of mass m = 4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell,as shown in the figure.If the cinder block accelerates downward at 4.90 m/s² when it is released,what is the mass M of the pulley?

A ball in the shape of a uniform spherical shell (like a soccer ball)of mass 1.5 kg and radius 15 cm rolls down a 35° incline that is 6.0 m high,measured vertically.The ball starts from rest,and there is enough friction on the incline to prevent slipping of the ball. (a)How fast is the ball moving forward when it reaches the bottom of the incline,and what is its angular speed at that instant? (b)If there were no friction on the incline,how fast would the ball be moving forward and what would be its angular speed at the bottom?

Through how many degrees does a 33 rpm turntable rotate in $0.32 \text { s? }$

A chicken is running in a circular path with an angular speed of 1.52 rad/s.How long does it take the chicken to complete one revolution?

A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s².The child is standing 4.65 m from the center of the merry-go-round.What is the magnitude of the linear acceleration of the child?

When a rigid object rotates about a fixed axis,what is true about all the points in the object? (There could be more than one correct choice.)

A uniform,solid,100-kg cylinder with a diameter of 1.0 m is mounted so it is free to rotate about fixed,horizontal,frictionless axis that passes through the centers of its circular ends.A 10-kg block is hung from a very light thin cord wrapped around the cylinder's circumference.When the block is released,the cord unwinds and the block accelerates downward,as shown in the figure.What is the acceleration of the block?

How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s²?

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round.As he does this,it is true to say that