Aim: How can we explain circular motion? Do Now: An object travels 5 m/s north and then travels 5 m/s east. Has the object accelerated?

Velocity is defined by two things: Magnitude (5 m/s) Direction (north) Direction has changed Therefore velocity has changed A change in velocity is defined as acceleration Up to now, we only dealt with linear acceleration (objects traveling in a straight line speeding up or slowing down) Changing direction – this is centripetal acceleration

In what direction does velocity act?  Velocity acts tangent to the circle made by the object. vv v v Demo

In what direction does acceleration act?  Acceleration acts inward, towards the center.

Is there a force?  Yes  Newton’s 2 nd law – unbalanced forces produce acceleration  If there is acceleration, there must be an unbalanced force  This is centripetal force

In what direction does the force act? The force acts inward, towards the center. FcFc FcFc FcFc FcFc Centripetal force and the centripetal acceleration are always pointing in the same direction

Centripetal force is not a separate force It is whatever force is pointing towards the center of the circle In this example, the normal force is pointing towards the center of the circle Therefore the normal force is the centripetal force

What is supplying the centripetal force? Spinning an object attached to a string in a circle Tension in the string Turning a car Friction between the tires and the road Ever drive and hit a patch of ice? No more friction -- no more turn The car skids in a straight line (tangent to the circle) Walking in a circle Friction between your shoes and the floor Ever try to run in dress shoes and make a sharp turn? OUCH!

If centripetal force is directed towards the center, why do you feel a “force” pushing you away from the center of the circle when in this motion, like turning in a car? The object gets pushed away from the center

Remember velocity? The object wants remain in motion tangent to the circle The car just gets in the way This gives the “illusion” of a force that really does not exist! Water in cup Demo (during lab)

How can we calculate centripetal acceleration?  Where v is the velocity and r is the radius of the circle traveled by the object

How do we calculate the centripetal force?  F = ma, so F c = ma c Substitute in a c =v 2 /r

A car whose mass is 500 kg is traveling around a circular track with a radius of 200 m at a constant velocity of 15 m/s. What is the centripetal acceleration? Given m = 500 kg r = 200 m v = 15 m/s a c = ? a c = 1.1 m/s 2 What is the centripetal force? F c = ? F c = ma c F c = (500 kg)(1.1 m/s 2 ) F c = 550 N

What if the velocity isn’t given?  The distance traveled by the object is the circumference of the circle; C = 2πr r

Example A 615 kg racing car completes one lap in 14.3 s around a circular track with a radius of 50.0 m. The car moves at a constant speed. (a) (a)What is the acceleration of the car? Given m = 615 kg d = c = 2πr t = 14.3 s r = 50 m a c =?

(a)What force must the track exert on the tires to produce this acceleration? Given m = 615 kg d = c = 2πr t = 14.3 s r = 50 m a c = 9.7 m/s 2 F c = ? F c = ma c F c = (615 kg)(9.7 m/s 2 ) F c = 5,965.5 N