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Uniform Circular Motion

Uniform Circular Motion. Uniform Circular Motion. Motion of an object moving in a circle at constant speed. The linear velocity vector for an object in uniform circular motion has a direction that is constantly changing. Therefore, the object experiences an acceleration.

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Uniform Circular Motion

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  1. Uniform Circular Motion

  2. Uniform Circular Motion • Motion of an object moving in a circle at constant speed. • The linear velocity vector for an object in uniform circular motion has a direction that is constantly changing. Therefore, the object experiences an acceleration.

  3. Centripetal Acceleration (ac) • The acceleration experienced by an object moving with uniform circular motion. It is directed toward the center of the circular path. ac = vt2 / r or ac = 4π2 r / T2

  4. Given: vt = 19.7 m/s r = 48.2 m Find: ac = ? ac = vt2 / r = (19.7 m/s)2 / (48.2 m) = 8.05 m/s2 Ex: A car moves at a constant speed of 19.7 m/s around a circular track that has a radius of 48.2 m. What is the centripetal acceleration of the car?

  5. Given: T = 13 s r = 6.0 m Find: ac = ? ac = 4π2 r / T2 = 4π2 (6.0 m) / (13 s)2 = 1.4 m/s2 Ex: A horse on a merry-go-round takes 13 s to make one complete rotation. If the horse is 6.0 m from the center, what is the centripetal acceleration?

  6. Centripetal Force (Fc) • The force that maintains circular motion. • The direction of Fc is toward the center of the circular path. • The centripetal force is not a special force. Any force (friction, normal force, tension force, gravity, etc.) can provide a centripetal force.

  7. Centripetal Force (Fc) • If ac is directed toward the center, and ∑ F = ma, then: Fc = mac Fc = mvt2 /r Fc = m4π2 r / T2

  8. Given: m = 70.5 kg vt = 30.0 m/s r = 100.0 m Find: Fc = ? Fc = mvt2 / r = 70.5 kg (30.0 m/s)2 /100.0 m = 634 N Ex: A 70.5 kg pilot is flying in a horizontal circle at a constant speed of 30.0 m/s. If the circle has a radius of 100.0 m, what is the centripetal force acting on the pilot?

  9. Given: m = 65 kg T = 13 s r = 6.0 m Find: Fc = ? Fc = m4π2 r / T2 = (65 kg) 4π2 (6.0 m)/(13 s)2 = 91 N Ex: A 65 kg person on a merry-go-round takes 13 s to make one complete rotation. If the person is 6.0 m from the center, what is the centripetal force acting on her?

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