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Uniform Circular Motion

Uniform Circular Motion. Circular Coordinates. r -radial. r.  -tangential. . Conditions. Uniform Circular motion occurs when an object is moving in a circular path at a constant speed. | v|=v. ● the instantaneous velocity v is always TANGENT to the path and a constant LENGTH. r.

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Uniform Circular Motion

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  1. Uniform Circular Motion

  2. Circular Coordinates r-radial r -tangential 

  3. Conditions Uniform Circular motion occurs when an object is moving in a circular path at a constant speed. |v|=v ● the instantaneous velocity v is always TANGENT to the path and a constant LENGTH r ● Since the speed is constant, there Is NO ACCELERATION in the tangential direction

  4. ● ALL of the ACCELERATION is perpendicular to the velocity vector and acts ONLY to change the velocity vector direction v a ● The direction of acceleration is RADIAL-it constantly changes but the magnitude stays the same ● This is called CENTRIPETAL ACCELERATION (centre-seeking)

  5. Instantaneous Acceleration Magnitude = instantaneous acceleration = speed = radius of circular path

  6. Applications: Orbital motion -planets about sun -moon, satellites about Earth Rotating Objects -wheels, vinyl records -amusement park rides (Windseeker!) -spinning a bucket over your head! -washing machine, centrifuge

  7. Example: A child on a merry go round is 3.0 m from the centre of the ride. If the child’s speed is 2.0 m/s, what is the magnitude of the child’s centripetal acceleration? Ans: V= 2.0 m/s r=3.0 m ac=? ac=v2/r = (2.0)2/3.0= 1.3 m/s2

  8. Question: The Earth travels around the Sun at a constant orbital speed. At any given point in its travel, the Earth’s acceleration is constant in magnitude and directed: tangentially forward along the path. tangentially backward along the path radially outwards away from the Sun radially inwards towards the Sun

  9. Question: On a merry go round, child A is 1.0 m from the centre while child B is 4.0 m from the centre, near the outer edge. How do the magnitudes of their tangential speeds compare? They are travelling at the same speed. A is travelling faster. B is travelling faster. Impossible to know without knowing the rate of rotation.

  10. Other forms of the Centripetal acceleration equation: Circumference, C=2r T= period, time for one complete revolution r Speed - We can rewrite the acceleration:

  11. Other forms of the equation:

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