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Uniform Circular Motion

Uniform Circular Motion. Basic Principles & Formulas. 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

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Uniform Circular Motion

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  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 v a r f

  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 or v² r

  7. Uniform Circular Motion Terms & Formulas • Force (F) = mv² r or m 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

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