Rotational Motion

1. Rotational Motion

2. Real objects have mass at points other than the center of mass. Each point in an object can be measured from an origin at the center of mass. If the positions are fixed compared to the center of mass it is a rigid body. Rigid Body ri

3. The motion of a rigid body includes the motion of its center of mass. This is translational motion A rigid body can also move while its center of mass is fixed. This is rotational motion. Translation and Rotation vCM 

4. Angular Acceleration • In uniform circular motion there is a constant radial acceleration. • ar = v2 / r = rw2 • If the angular velocity changes there is acceleration tangent to the circle as well as radially. The angular acceleration is a

5. The Effect of Torque • A tangential force on a mass creates an acceleration. • Tangential force: Ft = mat • Tangential acceleration: at = ra • The force is associated with a torque. • Torque: t = rFt Ft r m

6. Rotational Law of Acceleration • The force law can be combined with rotational motion. • Torque: t = rFt = r mat = m r2a • If torque replaces force, and angular acceleration replaces acceleration, this looks like the law of acceleration.

7. A rolling wheel is moving forward with kinetic energy. The velocity is measured at the center of mass. KCM = ½ mv2 A rolling wheel is rotating with kinetic energy. The axis of rotation is at the center of mass. Krot = ½ Iw2 Rotation and Translation w v

8. Rolling Energy • The energy of a rolling wheel is due to both the translation and rotation. • The velocity is linked to the angular velocity. • The effective energy is the same as a wheel rotating about a point on its edge. • Parallel axis theorem

9. A change in kinetic energy is due to work done on the wheel. Work is from a force Force acts as a torque Rolling down an incline the force is from gravity. Pivot at the point of contact The potential energy is converted to kinetic energy. Energy Conserved v R F = mg q next