Chapter 10 Rotation

Learning Objectives:

In this chapter you will basically learn:

\(\bullet\) Identify that if all parts of a body rotate around a fixed axis locked together, the body is a rigid body.

\(\bullet\) Apply the relationship between angular displacement and the initial and final angular positions.

\(\bullet\) Apply the relationship between average angular velocity, angular displacement, and the time interval for that displacement.

\(\bullet\) Apply the relationship between average angular acceleration, change in angular velocity, and the time interval for that change.

\(\bullet\) Given angular position as a function of time, calculate the instantaneous angular velocity at any particular time and the average angular velocity between any two particular times.

\(\bullet\) Given angular velocity as a function of time, calculate the instantaneous angular acceleration at any particular time and the average angular acceleration between any two particular times.

\(\bullet\) Relationship of the linear and angular variables.

\(\bullet\) Calculate the rotational kinetic energy of a body in terms of its rotational inertia and its angular speed.

\(\bullet\) Determine the rotational inertia of a body if it is given in Table 10-2.

\(\bullet\) Calculate the rotational inertia of a body by integration over the mass elements of the body.

\(\bullet\) Apply the parallel-axis theorem for a rotation axis that is displaced from a parallel axis through the center of mass of a body.

\(\bullet\) Identify that a torque on a body involves a force and a position vector, which extends from a rotation axis to the point where the force is applied.

\(\bullet\) Identify that a torque is assigned a positive or negative sign depending on the direction it tends to make the body rotate about a specified rotation axis: “clocks are negative.”

\(\bullet\) Apply Newton’s second law for rotation to relate the net torque on a body to the body’s rotational inertia and rotational acceleration, all calculated relative to a specified rotation axis.

\(\bullet\) Calculate the work done by a torque acting on a rotating body by integrating the torque with respect to the angle of rotation.

\(\bullet\) Apply the work–kinetic energy theorem to relate the work done by a torque to the resulting change in the rotational kinetic energy of the body.

\(\bullet\) Calculate the power of a torque at any given instant by relating it to the torque and the angular velocity at that instant.