Chapter 8Rotational Motion, Part 2

• Circular Motion

• Rotational Inertia

• Torque

• Center of Mass and Center of Gravity

• Centripetal/Centrifugal Force

• Angular Momentum

• Conservation of Angular Momentum

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Center of Mass/Center of Gravity

Physics Place VideosCenter of Mass Applet 2Center of Mass Applet 1

A baseball follows a smooth parabolic

trajectory.

A baseball Bat doesn’t’! It follows a wobbly trajectory.

But, the bat’s Center of Mass

follows a smooth parabolic trajectory.

Center of Mass: The average of the positions of all the mass in an object.The point of a body at which the force of gravity can be considered to act

A crescent wrench sliding across a frictionless surface follows a complicated motion, but its center of mass follows a straight line path.

Question 1

The broom balances at its center of gravity. I f you saw the broom into two parts through the center of gravity and then weigh each part on a scale, which part will weigh more?

1. Short broom part2. Long broom part

Centripetal ForceCentripetal Force is the force that makes an object move in a curved path.

Newton’s First Law: An object in motion will stay in motion with constant speed and direction unless acted on by an external force.

If a force doesn’t act, an object in motion will stay in motion in a straight line.

Examples:

The centripetal force that makes the airplane move in a circle is exerted on the wings by air moving over them.

The can moves in a circle because of the force exerted on it by the rope

The force exerted radially inward by friction on the tires makes the car move in a circle.

Question 2Does a centripetal force do work on an object?

A. Yes

B. No

C. Only on Tuesdays

Angular MomentumWe have learned that if an object has inertia and it’s in motion, we can describe it’s “momentum” as its mass times its velocity (momentum = mv).

Similarly, a rotating object has rotational inertia and also has a rotational momentum, called “Angular Momentum”.

Angular momentum depends on an object’s rotational inertia and rotational velocity:

Angular momentum = Rotational Inertia x Rotational Velocity

- Or - Angular momentum = I

If an object is in revolution around an external point, its angular momentum can be expressed as:

Angular momentum = mvrr

v

m

Conservation of Angular Momentum

In linear motion, to gain or lose momentum, an impulse must be delivered to an object. If no impulse acts, the momentum of the object (or system) doesn’t change … momentum is conserved.

In rotational motion, Angular Momentum is conserved.

If no external net torque acts on a rotating system, the angular momentum of that system remains constant.

Large Rotational InertiaSmall Rotational Velocity

Small Rotational InertiaLarge Rotational Velocity