1. Uniform Circular Motion

2. Motion of an object moving in a circle at constant speed. Motion of an object moving in a circle at constant speed. The linear velocity vector for an object in uniform circular motion has a direction that is constantly changing. Therefore, the object experiences an acceleration. The linear velocity vector for an object in uniform circular motion has a direction that is constantly changing. Therefore, the object experiences an acceleration.

3. Centripetal Acceleration (a c ) The acceleration experienced by an object moving with uniform circular motion. It is directed toward the center of the circular path. The acceleration experienced by an object moving with uniform circular motion. It is directed toward the center of the circular path. a c = v t 2 / r or a c = 4π 2 r / T 2

4. Ex: A car moves at a constant speed of 19.7 m/s around a circular track that has a radius of 48.2 m. What is the centripetal acceleration of the car? Given: v t = 19.7 m/s r = 48.2 m r = 48.2 m Find: a c = ? a c = v t 2 / r = (19.7 m/s) 2 / (48.2 m) = 8.05 m/s 2

5. Ex: A horse on a merry-go-round takes 13 s to make one complete rotation. If the horse is 6.0 m from the center, what is the centripetal acceleration? Given: T = 13 s r = 6.0 m r = 6.0 m Find: a c = ? a c = 4π 2 r / T 2 = 4π 2 (6.0 m) / (13 s) 2 = 1.4 m/s 2

6. Centripetal Force (F c ) The force that maintains circular motion. The force that maintains circular motion. The direction of F c is toward the center of the circular path. The direction of F c is toward the center of the circular path. The centripetal force is not a special force. Any force (friction, normal force, tension force, gravity, etc.) can provide a centripetal force. The centripetal force is not a special force. Any force (friction, normal force, tension force, gravity, etc.) can provide a centripetal force.

7. Centripetal Force (F c ) If a c is directed toward the center, and If a c is directed toward the center, and ∑ F = ma, then: F c = ma c F c = mv t 2 /r F c = m4π 2 r / T 2

8. Ex: A 70.5 kg pilot is flying in a horizontal circle at a constant speed of 30.0 m/s. If the circle has a radius of 100.0 m, what is the centripetal force acting on the pilot? Given: m = 70.5 kg v t = 30.0 m/s v t = 30.0 m/s r = 100.0 m r = 100.0 m Find: F c = ? F c = mv t 2 / r = 70.5 kg (30.0 m/s) 2 /100.0 m = 634 N

9. Ex: A 65 kg person on a merry-go-round takes 13 s to make one complete rotation. If the person is 6.0 m from the center, what is the centripetal force acting on her? Given: m = 65 kg T = 13 s T = 13 s r = 6.0 m r = 6.0 m Find: F c = ? F c = m4π 2 r / T 2 = (65 kg) 4π 2 (6.0 m)/(13 s) 2 = 91 N