Ch 8 : Rotational Motion 

Rotational Inertia Depends on the distribution of mass with respect to the axis of rotation. M M R R I = MR2 I = MR2

M R M L I = ½ MR2

R L

R

Torque o = R F R F R = Lever Arm A force times the perpendicular distance to the point of rotation (Lever Arm) R o = R F F R = Lever Arm

R o F o = R F F R = Lever Arm

Center of Mass and Center of Gravity The point on an object where all of its mass can be considered to be concentrated. The point on an object where all of its weight can be considered to act. Center of Gravity These are the same point for an object in a constant gravitational field.

Center of Mass M M L/2 L/2 L 3M Center of Mass M 1/4L 3/4L L

The center of mass lies at the geometric center for a symmetric, uniform density object.

The center of mass can be outside the mass of the body.

Stability Less Stable Equilibrium Stable Equilibrium

Centripetal Force v Fc 

Simulated Gravity R 

Angular Momentum = Rotational Inertia x Angular velocity  M R I = MR2

Conservation of Angular Momentum 2 1 R R/2 L = mR21 L = m(R/2)22