Rotational Motion Tangential and Rotational Velocity Tangential and

Rotational Motion

Tangential and Rotational Velocity

Tangential and Rotational Velocity What happens to the tangential velocity as the distance from the center increases? Try a thought experiment: Picture yourself on a merry-go-round. How fast are you going on the outside edge. Now, walk towards the center. What happens to your linear speed as you walk? What is your linear speed at the center?

Centripetal and Centrifugal Force Now, think about the force that you feel pulling you toward the outside edge of the merry-go-round. As you walk toward the center, what happens to the magnitude of that force? What is the force at the center?

Big Idea #1 Tangential speed, centripetal force, and the fictitious centrifugal force all decrease as you move towards the axis of rotation. They are zero at the axis of rotation.

Consider this: A candle is placed near the edge of a rotating platform, and the flame is shielded so that air will not affect it, what’s up with the flame? Will it point straight up, back, forward, to the center, or to the outside?

Big Idea #2: Centripetal force points to the axis of rotation (to the center of the circle).

Centripetal Force and Orbits We have established that centripetal force points to the center of the circle. So why does a satellite not crash into the Earth?

Big Idea #3: The reason is – the satellite has inertia. Its orbital velocity combines with centripetal force to create a stable orbit. Inertia + centripetal force = Orbit! Orbital Velocity + centripetal force = Orbit!

Torque and the Lever Arm

Consider this: What happens if one of the see-saw riders moves toward the center?

Answer They will rise and the other rider will fall. Why?

Big Idea #4 Rotational acceleration is produced by torque, “the turning force. ” Torque increases as the lever arm increases. Balanced torques (clockwise/counterclockwise) produce no angular acceleration.

Big Idea #5 Conservation of Angular Momentum – in the absence of a net torque, angular momentum is constant. What happens to a spinning figure skater if they pull their arms in close to their body?

Answer: They spin faster. Why? Conservation of Angular Momentum! L = mvr Holding L constant, what must happen to v as r decreases?