Exam 9: Rotational Motion

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,

A solid ball of mass 1.0 kg and radius 10 cm rolls with a forward speed of 10 m/s when it comes to a hill.There is enough friction on the hill to keep the ball from slipping as it rolls up. (a)How high vertically up the hill can the ball roll before coming to rest? (b)How high vertically could the ball go if the hill were totally frictionless? (c)How is it that the ball can go higher with friction than without friction?

A machinist turns on the power to a grinding wheel at time t = 0 s.The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of $38 \mathrm { rad } / \mathrm { s }$ The wheel is run at that angular speed for 30 s and then power is shut off.The wheel slows down uniformly at 2.1 rad/s² until the wheel stops.In this situation,what is the angular acceleration of the wheel between t = 0 and t = 10s?

A bowling ball of mass 7.5 kg and diameter 18 cm rolls without slipping down a 10-m bowling lane with a constant speed 4.3 m/s. (a)Through what angle does the bowling ball turn as it travels the length of the lane? (b)What is the angular speed of the bowling ball? (c)Calculate the maximum radial acceleration that a point on the surface of the bowling ball could have. (d)Calculate the tangential acceleration of a point on the surface of the bowling ball.

An old LP record that is originally rotating at 33.3 rad/s has a uniform angular acceleration of 2.15 rad/s².Through what angle has the record turned when its angular speed reaches 72.0 rad/s?

A small ball is tied to one end of a light 2.5-m wire,and the other end of the wire is hooked to the ceiling.A person pulls the ball to the side until the wire makes an angle of 35° with the plane of the ceiling and then gently releases it.What is the angular speed of the ball,in rad/s,as it swings through its lowest point?

A wheel having a moment of inertia of 5.00 kg ∙ m² starts from rest and accelerates under a constant torque of 3.00 N ∙ m for 8.00 s.What is the wheel's rotational kinetic energy at the end of 8.00 s?

A solid uniform sphere of mass 120 kg and radius 1.7 m starts from rest and rolls without slipping down an inclined plane of vertical height 5.3 m.What is the angular speed of the sphere at the bottom of the inclined plane?

An electrical motor spins at a constant $2695.0 \mathrm { rpm }$ If the rotor radius is $7.165 \mathrm {~cm}$ what is the linear acceleration of the edge of the rotor?

A potter's wheel has the shape of a solid uniform disk of mass $7.0 \mathrm {~kg}$ and radius 0.65 m.It spins about an axis perpendicular to the disk at its center.A small 2.1 kg lump of very dense clay is dropped onto the wheel at a distance 0.41 m from the axis.What is the moment of inertia of the system about the axis of spin?

A puck moves on a horizontal air table.It is attached to a string that passes through a hole in the center of the table.As the puck rotates about the hole,the string is pulled downward very slowly and shortens the radius of rotation,so the puck gradually spirals in towards the center.By what factor will the puck's angular speed have changed when the string's length has decreased to one-half of its original length?

An artificial satellite in a low orbit circles the earth every 98 minutes.What is its angular speed in rad/s?

The L-shaped object shown in the figure consists of three small mass spheres connected by thin uniform rods,each rod of mass 3.00 kg.Assume that the masses shown are accurate to three significant figures.What is the moment of inertia of this object (a)about the x-axis,and (b)about the y-axis?

A uniform,solid,cylindrical flywheel of radius 1.4 m and mass 15 kg rotates at $2.7 \mathrm { rad } / \mathrm { s }$ What is the magnitude of the flywheel's angular momentum?

A machinist turns on the power on to a grinding wheel at time t = 0 s.The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of $58 \mathrm { rad } / \mathrm { s }$ The wheel is run at that angular velocity for 30 s,and then power is shut off.The wheel slows down uniformly at $1.4 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops.What is the total number of revolutions made by the wheel in this situation?

A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg ∙ m² and a radius of 12.5 cm.An object of mass of 423 g is attached to the free end of the string.With the string vertical and taut,the object is gently released so it can descend doe to the gravitational force exerted on it by Earth.As the object descends,the string unwinds and causes the pulley to rotate,but does not slip on the pulley.What is the speed of the object after it has fallen through 1.25 m?

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

What is the angular speed,in rad/s,of a flywheel turning at 813.0 rpm?

Three solid,uniform,cylindrical flywheels,each of mass 65.0 kg and radius 1.47 m,rotate independently around a common axis through their centers.Two of the flywheels rotate in one direction at 8.94 rad/s,but the other one rotates in the opposite direction at 3.42 rad/s.Calculate the magnitude of the net angular momentum of the system.

Two children,Ahmed and Jacques,ride on a merry-go-round.Ahmed is at a greater distance from the axis of rotation than Jacques.Which of the following are true statements? (There could be more than one correct choice.)