1. Uniform Circular Motion Basic Principles & Formulas

2. Uniform Circular Motion Principles Object moving at a constant speed (scalar) Object’s velocity is constantly changing due to a continuous change in direction Velocity is tangent is to circular motion While in motion, there is a force and an acceleration being applied to the object

3. Uniform Circular Motion Questions While moving in a circular path, if string breaks, in what direction will the object travel? In a straight line, perp. to radius (Law of Inertia) In what direction is the force? Inward In what direction is the acceleration? Inward

4. Uniform Circular Motion Diagram Acceleration & Force = Parallel to Radius / Velocity = Perpendicular to Radius r v f a

5. Uniform Circular Motion Terms & Formulas Period (T) = time it takes to make 1 revolution Period may be given, obvious or determined by time/revolutions ex. 25 rev. in 10 sec. T = 10/25 .4 sec (T = 1/f) Frequency (f) = number of revolutions made in 1 sec. (f = 1/T) units = Hz

6. Uniform Circular Motion Terms & Formulas Velocity (v) =2πr T Acceleration (a) =4π²r T² orv² r

7. Uniform Circular Motion Terms & Formulas Force (F) =mv² r orm 4π²r T²

8. UCM Example Problem A 615 kg race car completes 1 lap in 14.3 sec around a circular track with a radius of 50.0 m. What is the car’s T, f, v, a, F (on tires)? T = 14.3/1 = 14.3 f = 1/14.3 = 0.07 Hz

9. UCM Example Problem (cont.) V = (2)(π)(50.0) 14.3 = 21.97 m/s a = (21.97 m/s)² 50.0 = 9.65 m/s²

10. UCM Example Problem (cont.) F (on tires) = (615 kg)(21.97 m/s)² 50.0 m = 5,936 N