Chapter 11 Rolling, Torque & Angular Momentum

Learning Objectives:

In this chapter you will basically learn:

\(\bullet\) Identify that smooth rolling can be considered as a combination of pure translation and pure rotation.

\(\bullet\) Apply the relationship between the center-of-mass speed and the angular speed of a body in smooth rolling.

\(\bullet\) Calculate the kinetic energy of a body in smooth rolling as the sum of the translational kinetic energy of the center of mass and the rotational kinetic energy around the center of mass.

\(\bullet\) Apply the relationship between the center-of-mass acceleration and the angular acceleration.

\(\bullet\) For smooth rolling of an object up or down a ramp, apply the relationship between the object’s acceleration, its rotational inertia, and the angle of the ramp.

\(\bullet\) Calculate the torque due to a force on a particle by taking the cross product of the particle’s position vector and the force vector, in either unit-vector notation or magnitude-angle notation.

\(\bullet\) Calculate the angular momentum of a particle by taking the cross product of the particle’s position vector and its momentum vector, in either unit-vector notation or magnitude-angle notation.

\(\bullet\) Apply Newton’s second law in angular form to relate the torque acting on a particle to the resulting rate of change of the particle’s angular momentum, all relative to a specified point.

\(\bullet\) Apply the relationship between the angular momentum of a rigid body rotating around a fixed axis and the body’s rotational inertia and angular speed around that axis.

\(\bullet\) When no external net torque acts on a system along a specified axis, apply the conservation of angular momentum to relate the initial angular momentum value along that axis to the value at a later instant.

\(\bullet\) Identify that the gravitational force acting on a spinning gyroscope causes the spin angular momentum vector (and thus the gyroscope) to rotate about the vertical axis in a motion called precession.

\(\bullet\) Identify that a gyroscope’s precession rate is independent of the gyroscope’s mass.

11.1 The Kinetic Energy of Rolling, The Forces of Rolling, Torque, Angular Momentum.

(Solved Problems: 7, 9, 12, 24, 26, 33, 36)