1. Rotational Motion

2. The Effect of Torque  A tangential force on a mass creates an acceleration. Tangential force: F t = m a tTangential force: F t = m a t Tangential acceleration: a t = r Tangential acceleration: a t = r   The force is associated with a torque. Torque:  = r F tTorque:  = r F t r FtFt m

3. Rotational Law of Action  The force law can be combined with rotational motion. Torque:  = r F t = r m a t = m r 2 Torque:  = r F t = r m a t = m r 2   If torque replaces force, and angular acceleration replaces acceleration, this looks like the law of action.

4. Rotational Inertia  The term mr 2 takes the place of mass in the rotational law of action.  This is called the rotational inertia or moment of inertia. The symbol is IThe symbol is I  For a single mass at a distance: I = mr 2.

5. Pendulum Torque  The tangential force on a pendulum is due to gravity. F t = mg sin F t = mg sin   Tangential acceleration: a t = g sin  = L a t = g sin  = L   = g sin  / L  = g sin  / L  Torque:  = r F t = mgL sin   = r F t = mgL sin   The torque is related to the moment of inertia. I =  /  = ( mgL sin  g sin  / L I =  /  = ( mgL sin  g sin  / L  I = mL 2I = mL 2 L F t = mgsin  mg 

6. Torque and Work  A force does work on an object acting over a distance.  A torque does work on an object rotating through an angle. r 

7. Conservation of Energy  The net work done by forces on an object equals the change in kinetic energy.  The net work done by torques on an object equals the change in rotational kinetic energy.

8. Rotational Power  As with translational motion, power is the rate of work done.  The earth is slowing due to the tides. About 28 s / century 1 part in 10 8  The kinetic energy is changing.  K = I   The power dissipation is large: About 7 billion hp next