Exam 8: Rotational Motion and Equilibrium

A ball is attached to a string and revolves in a horizontal circle with angular momentum. When the string breaks at point B on the circumference, the ball moves off tangentially along path B-Q. As it moves along B-Q, increasing its distance from the center of the circle, its angular momentum

State the conservation of angular momentum.

A triatomic molecule is modeled as follows: mass m is at the origin, mass 2m is at x = a, and mass 3m is at x = 2a. (a) What is the amount of inertia about the origin? (b) What is the moment of inertia about the center of mass?

What condition or conditions is/are necessary for rotational equilibrium?

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

A sphere of radius R and mass M is released from rest, and rolls without slipping down a plane inclined at angle G above horizontal. What is the speed of the sphere after it has moved a distance L?

A wheel slows down uniformly and comes to rest in 15. seconds. It is rotating initially at 2.0 revolutions per second and has a diameter of 50.cm. (a) What was the centripetal acceleration at the instant when it was rotating initially? (b) What was the tangential acceleration?

A potter's wheel with a moment of inertia of 8.0 kg-m² has 5.0 N-m applied to it. It starts from rest. 10. s later it has gained what kinetic energy?

Consider a rigid body that is rotating. Which of the following is an accurate statement?

An 8.0 kg-m² wheel with 155. Joules of rotational kinetic energy requires what torque to bring it to rest in 4.0 s?

If an object is in unstable equilibrium, any small displacement results in a restoring force or torque, which tends to return the object to its original equilibrium position.

A pencil balanced on its tip such that it does not move

What condition or conditions is/are necessary for static equilibrium?

Consider a solid object which is subjected to a net torque. That object will experience which of the following?

A solid cylinder and a hollow cylinder have the same mass and the same radius. Which statement is true concerning their moment of inertia about an axis through the exact center of the flat surfaces?

We can best understand how a diver is able to control his rate of rotation while in the air (and thus enter the water in a vertical position) by observing that while in the air

A ball, solid cylinder, and a hollow pipe all have equal masses and radii. If the three are released simultaneously at the top of an inclined plane, which will reach the bottom first?

A 2.50 kg is at ( 1.00, 3.00) meters. What is the moment of inertia: (a) about the x-axis? (b) about the y-axis? (c) about the line defined by x= 6.00 m?

State the condition of stable equilibrium.

Consider a motorcycle of mass 150. kg, one wheel of which has a mass of 10. kg and a radius of 30. cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.