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Uniform Circular Motion

Learn about uniform circular motion, including concepts like angular speed, tangential velocity, centripetal force, and key points to understand the dynamics of objects moving in circular paths.

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Uniform Circular Motion

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  1. Uniform Circular Motion An object going in a circle at a constant speed. Question: is an object that is undergoing uniform circular motion accelerating?

  2. rotation • rotation: when an object spins or rotates around an internal axis. Example: A krispy kreme rotating around a straw.

  3. Revolution • revolution: when an object turns or revolves around an external axis. Example: A planet revolving around a star. • period: the time for one revolution • Noted as T

  4. Linear speed • linear speed: distance moved per unit of time (speed).

  5. Tangential Speed • tangential speed (Vt) : the speed of an object that is moving along a circular path. The direction of motion is tangent to the circle. • Depends on the circle radius. • Larger radius means the speed is greater. • Smaller Radius means speed is less

  6. Which will have the greatest speed?

  7. Angular speed • angular speed (w): the number of rotations per unit of time. Also called rotational speed.

  8. Centripetal Force • centripetal force (Fc): any force that will cause an object to take a circular path.

  9. Frequency and period • Frequency: number of revolutions (turns) per time unit (usually seconds). • Noted as f • Frequency: number of events (revolutions) time • The frequency and period are reciprocals of each other

  10. Key Points for Uniform Circular Motion • All points on a rotating rigid object will have the same angular speed (and thus the same angular acceleration). • The tangential speed of an object placed on a rotating body will increase as it is moved away from the center of the rigid body. • An object that is following a circular path has a net force (Fc) and acceleration (ac) that are acting towards the center of the object.

  11. Key points continued • Velocity is always tangent to the circle and is always changing. • Acceleration goes towards the center of the circle • Look at the following rotating disk. Which point has the greater tangential velocity? Which point has the greater angular velocity?

  12. Formulas • Equations: • ac = vt2 Fc = mac = mvt2 • r r • vt = rww must be in radians per time unit • Ac = rw2 • Reminders: • 1 revolution = 360 degrees = 2 p rad • for one revolution v = d = 2 p r • t T

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