10 4 Rotation with Constant Angular Acceleration v

10 -4 Rotation with Constant Angular Acceleration v = v 0 + at Kinematic Equations ω = ω0 + αt x-x 0 = ½(v + v 0)t θ- θ 0 = ½(ω + ω0)t v 2 = v 02 + 2 a(x-x 0) ω2 = ω02 + 2α(θ- θ 0) x-x 0 = v 0 t + ½ at 2 θ- θ 0= ω0 t + ½ αt 2 x-x 0 = vt - ½ at 2 θ- θ 0= ωt - ½ αt 2 • 12 The angular speed of an automobile engine is increased at a constant rate from 1200 rev/min to 3000 rev/min in 12 s. (a) What is its angular acceleration in revolutions per minute-squared? (b) How many revolutions does the engine make during this 12 s interval?

10 -5 Relating the Linear and Angular Variables

10 -6 Kinetic Energy of Rotation K = ½ Iω2

10 -7 Calculating the Rotational Inertia If a rigid body consists of a few particles, we can calculate its rotational inertia about a given rotation axis with the following equation: If a rigid body consists of a great many adjacent particles (it is continuous, like a Frisbee), we replace the sum in the above equation with an integral and define the rotational inertia of the body as:

Rotational Inertias of continuous Objects

Parallel-Axis Theorem The parallel-axis theorem relates the rotational inertia I of a body about any axis to that of the same body about a parallel axis through the center of mass, where h is the perpendicular distance between the two axes.