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Uniform Circular Motion

Uniform Circular Motion. Acceleration. When an object moves at a constant speed in a circular path, it is constantly changing direction – accelerating. Δv. Centripetal Acceleration. Δv always points to the center of the circle

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Uniform Circular Motion

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  1. Uniform Circular Motion

  2. Acceleration • When an object moves at a constant speed in a circular path, it is constantly changing direction – accelerating Δv

  3. Centripetal Acceleration • Δv always points to the center of the circle • Since a = Δv/t, a must also be pointed to the center of the circle • Centripetal Acceleration – center seeking acceleration • Also called Radial Acceleration – directed along the radius • Symbol - ar

  4. Equation • ar = v2 / r • v is the velocity and r the radius • Greater v, faster direction changes, greater the ar • Greater r, less rapidly changing direction, lower the ar

  5. v and a are always perpendicular to one another at any given point on a circle v a

  6. Frequency and Period • Circular motion is often described in terms of frequency (f) and period (T) • Frequency – revolutions per sec – unit Hz • Period – time for one revolution – unit sec • The velocity is the distance traveled per time

  7. Distance is the circumference of the circle which is 2π r • v = 2π r / T

  8. Example 1 • A 150 g ball at the end of a string is revolving in a horizontal circle of radius .600 m. The ball makes 2.00 revolutions in a second. What is the centripetal acceleration?

  9. Example 2 • The moon’s nearly circular orbit about the earth has a radius of about 384000 km and a period of 27.3 days. Determine the acceleration of the moon toward the earth.

  10. Force • Objects accelerating must have a force acting on them therefore there must be a force keeping an object in a circular path • This force is called Centripetal Force (Fr) • Fr = mar = mv2 / r

  11. Since ar is directed into the center of the circle, so is Fr • This force is always applied by other objects

  12. Factious Force • There is no force pulling objects out from the center of a circle • There is an illusion of an outward force caused by inertia • This factious force is called centrifugal force

  13. Example 3 • What force must a person exert on a string attached to a .150 kg ball in order to keep it revolving in a horizontal circle of radius .600 m ? The ball makes 2.00 revolutions per second.

  14. Example 4 • In a tetherball game a .85 kg ball is hit in a horizontal circle around a pole. The rope makes an angle of 35° with the pole and is holding the ball with a tension of 12.5 N. The radius of its circular path is 1.25 m. Find the centripetal acceleration, centripetal force, the velocity, and period.

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