1. Physics 101: Lecture 10, Pg 1 Physics 101: Lecture 10 Application of Newton's Laws l New Material: Textbook Chapter 5 è Circular Motion & Centripetal Acceleration

2. Physics 101: Lecture 10, Pg 2 You are twirling a ball on string. What happens if the string breaks ? a b c Answer: b v

3. Physics 101: Lecture 10, Pg 3 Acceleration in Uniform Circular Motion (circular motion with constant speed) vv1vv1 vv2vv2 vvvv vv2vv2 vv1vv1 R RRRR centripetal acceleration a  v a ave =  v /  t Uniform motion: magnitudes of v1,v2 are equal: v 1 =v 2 =v Distance traveled (small  t) :  R = v Distance traveled (small  t) :  R = v  t Similar triangles:  R/R =  v/v =>  v/  t= v 2 /R

4. Physics 101: Lecture 10, Pg 4 Uniform Circular Motion (circular motion with constant speed) v R centripetal acceleration Instantaneous velocity is tangent to circle Instantaneous acceleration is radially inward There must be a force to provide the acceleration a

5. Physics 101: Lecture 10, Pg 5 Example: Circular Motion Suppose you are driving through a valley whose bottom has a circular shape. If your mass is m, what is the magnitude of the normal force F N exerted on you by the car seat as you drive past the bottom of the hill 1. F N mg v mg FNFN R  F = ma = mv 2 /R  F = F N - mg=mv 2 /R F N = mg + mv 2 /R a=v 2 /R correct When level your normal force = your weight Since there is centripetal acceleration, the normal force is greater than simply mg.

6. Physics 101: Lecture 10, Pg 6 Centripetal Force Define frequency f, period T, angular velocity  : Centripetal acceleration: Acceleration is the result of a net-force acting on an object. In case of a c this net-force is called centripetal force, F c : Magnitude of F c : F c =  F= m a c = m v 2 /R