Exam 8: Rotational Motion and Equilibrium

Two children, each of mass 20.0 kg, ride on the perimeter of a small merry-go-round that is rotating at the rate of 1.0 revolution every 4.0 s. The merry-go-round is a disk of mass 30. kg and radius 3.0 m. The children now both move halfway in toward the center to positions 1.5 m from the axis of rotation. Calculate the kinetic energy before and after, and the final rate of rotation. Explain any changes in energy.

A planet speeds up in its orbit as it gets closer to the sun because of

A uniform solid cylinder (mass 100. kg and radius 50.0 cm) is mounted so it is free to rotate about fixed horizontal axis that passes through the centers of its circular ends. A 10.0 kg block is hung from a massless cord wrapped around the cylinder's circumference. When the block is released, the cord unwinds and the block accelerates downward, as shown in Figure 8-2. What is the block's acceleration?

Moment of Inertia has which of the following units?

"Lever Arm" can have which of the following units?

A 50. cm diameter wheel is rotating initially at 2.0 revolutions per second. It slows down uniformly and comes to rest in 15. seconds. (a) What was its angular acceleration? (b) Through how many revolutions did it turn in those 15. s?

Unbalanced torques produce rotational accelerations, and balanced torques produce rotational equilibrium.

The condition for rolling without slipping is that the center of mass speed is

A car is traveling along a highway at 65 mph. What is the linear speed of the top of the tires?

Consider a car with its wheels rolling (not sliding) on the road. How fast must the auto move for some point on a wheel to reach the speed of sound? Explain.

A cylinder of radius R and mass M rolls without slipping down a plane inclined at an angle θ above horizontal. (a) What is the torque about the point of contact with the plane? (b) What is the moment of inertia about the point of contact? (c) What is the linear speed of the cylinder t seconds after it is released from rest?

Initially, a 2.00-kg mass is whirling at the end of a string (in a circular path of radius 0.750 m) Figure 8-9 The string has been slowly winding around a vertical rod, and a few seconds later the length of the string has shortened to 0.250 m. What is the instantaneous speed of the mass at the moment the string reaches a length of 0.250 m?

A cylinder, of radius 8.0 cm, rolls 20. cm in 5.0 s. Through what angular displacement does the cylinder move in this time?

A heavy seesaw is out of balance. A lightweight girl sits on the end that is tilted downward, and a heavy boy sits on the other side so that the seesaw now balances. If the boy and girl both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw?

A boy and a girl are balanced on a massless seesaw. The boy has a mass of 60 kg and the girl's mass is 50 kg. If the boy sits 1.5 m from the pivot point on one side of the seesaw, where must the girl sit on the other side for equilibrium?

An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation?

A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

Consider two uniform solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

A wheel of 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?

The moment of inertia of a solid cylinder about its axis is given by 0.5MR². If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is