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Circular Motion

Circular Motion. Principles of Physics. r. When an object moves in a circle its path is described by:   Radius (r) – distance from the center to the perimeter (meters) Circumference (C) – perimeter of circle (2πr) (meters)

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Circular Motion

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  1. Circular Motion Principles of Physics

  2. r When an object moves in a circle its path is described by:   Radius (r) – distance from the center to the perimeter (meters) Circumference (C) – perimeter of circle (2πr) (meters) Period (T) – time to go around the circle once (seconds)

  3. Rotational Speed vs Linear Speed Rotational Speed (scalar quantity) • number of times around the circle per unit time (rot/s) Linear Speed (v) • Distance per unit time

  4. Rotational Speed vs Linear Speed Example: An object is moving around a circle of radius 5m. It completes 5 rotations every second. How fast is it going?

  5. Centripetal Force • Assume linear speed (what the speedometer in your car would read) is not changing during motion in a circle • Speed is constant • Direction is changing • If velocity is changing then the object is accelerating • If the object is accelerating then an unbalanced force must be acting on it Changing Velocity

  6. Centripetal Force Remember: Newton’s 1st Law → objects in motion stay in motion in straight lines unless a force is acting So, A force must be acting on an object if it is travelling in along a circular path Special name – centripetal force (Fc) (centripetal = center seeking) **No such thing at centrifugal or centrifical force

  7. Centripetal Force • To move in circles the direction of the force is always changing, but always directed toward the center of the circular path. v • Fc, ac

  8. Centripetal Force Centripetal force is another name for any force that causes an object to move in circles Therefore, Any type of force can be a centripetal force Example: friction keeps cars moving around circular ramps when entering or exiting the highway.

  9. Calculating Centripetal Force We know: F = ma, so Fc = mac ac = centripetal acceleration = v2/r so, Fc = mac = mv2/r Fc = macac = v2/r Fc = mv2/r

  10. Example 1: A 1.0 kg ball attached to a string 0.50 m long is swung in a circle. Its speed along the circular path is 6.0 m/s. What are ac and Fc? m = 1 kg r = 0.5 m v = 6 m/s ac = v2/r = (6m/s)2 /0.5 m = 72 m/s2 Fc = mac = 1 kg (72 m/s2) = 72 N

  11. Example 2: Suppose a 5 kg object is being held in a circular path of radius 20 m with a force of 400 N. What is the speed of the object? Fc = mv2 r 400 = 5v2 20 400(20) = 5v2 5 5 1600 = v2 v = 40 m/s m = 5 kg r = 20 m F = 400 N

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