Circular Motion AP Physics Mrs Coyle Rotation vs

Circular Motion AP Physics Mrs Coyle

Rotation vs Revolution • Earth rotates about its axis • Satellite revolves about the earth.

Uniform Circular Motion n Linear(tangential)speed, v, is constant.

-Tangential Velocity -Centripetal Acceleration -The tangential velocity vector is tangent to the circle at the point of study. v= 2 pr/T = 2 prf = d/t v v -Centripetal Acceleration: points to center a= v 2 / r

How does the v vary with r? The linear speed increases as r increases. Example: n How does your linear speed change when you are on a merry-go-round and you move away from the center? n

How does the f vary with r? n f does not depend on r Example: n How does your frequency change when you are on a merry-go-round and you move away from the center?

Centripetal Force, Fc= m v 2 r n n n Is a center seeking force. (Always points to the center. ) Is perpendicular to the tangential velocity at any given instant. It is not an extra force. It is an existing force(s) that point(s) to the center.

What force represent s the centripetal force for a coin on a record player?

What force plays the role of the centripetal force when a car rounds a curve?

Car Rounding a Bend (Flat Road)

Example 1: Car Rounding a Curve n n A car is travelling with a speed of 45 km/h on a circular horizontal track of radius 50 m. What is the minimum coefficient of friction, so that the car stays on the track? Answer: 0. 3

Rotor Ride

Rotor Ride n http: //www. youtube. com/watch? v=J 7 k 8 Oz _73 mw&feature=player_embedded#

What force plays the role of the centripetal force in the rotor ride? n http: //upload. wikimedia. org/wikipedia/commons/7/7 d/Rotormidcyclelunapraksyd. JPG

Example 2: Rotor n A brave student rides in a rotor of radius 5 m whose floor drops when it reaches a speed of 20 mi/h. What is the coefficient of friction between the student and the wall of the rotor, so that the student does not fall? Answer: 0. 6

What forces represent the centripetal force for a child on this ride?

Example 3 Conical Pendulum Find an expression for v in terms of L and q. ______ Ans: v=√Lgsin q tan q

n Can q be 90 o for a conical pendulum? (Can there be a horizontal circular path when twirling a ball)?

Example 4 Car on a banked road At what angle should the road be banked if a car is to safely round the curve at a speed of 13. 4 m/s and the radius of the curve is 50 m if friction is neglected? Ans: 20. 1 o

Non-Uniform Circular Motion n n v tangential is not constant. There are both tangential and radial accelerations and therefore forces.

What force plays the role of the centripetal force when a ball is on the top of a loop-the-loop?

Loop the Loop

Example 5: Loop-the-loop n n What is the critical velocity of a ball at the top of the loop of radius. 3 m so that it completes the loop? Answer: 1. 7 m/s