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Uniform Circular Motion

Uniform Circular Motion. Year 1 Dynamics. P’. s. . O. r. P. Angular Displacement. Consider a particle at point P on a rotating disc of radius r. if disc turns through 1 rev, P travels a distance s=2 r if disc turns through 1/(2) revs, P travels a distance s=r.

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Uniform Circular Motion

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  1. Uniform Circular Motion Year 1 Dynamics

  2. P’ s  O r P Angular Displacement • Consider a particle at point P on a rotating disc of radius r. • if disc turns through 1 rev, P travels a distance s=2r • if disc turns through 1/(2) revs, P travels a distance s=r • We define this particular angle to be 1 radian (1 rad) • if disc turns through 1 rad, then s=r • if disc turns through  rad, then s=r • (1 rev = 3600=2 rad)

  3. P’ vT  O r P Angular Velocity Just as so (rad s-1 (SI), rpm, deg/sec) As P moves to P’, its instantaneous tangential velocity is:

  4. ry r  rx x Acceleration in Uniform Circular Motion y To find the velocity differentiate once: Therefore v is perpendicular to r, as expected.

  5. Acceleration in Uniform Circular Motion To find the acceleration, differentiate again: The acceleration is parallel to the radius, but in the opposite direction. “CENTRIPETAL ACCELERATION”

  6. Acceleration in Uniform Circular Motion Since v=r, then =v/r and so a= 2r = v2/r For the case of the centrifuge, we estimate that the length of the arm is approximately 5m and the acceleration (Paul) was 3g. The angular velocity to give this acceleration is: 2 = a/r =>  = 2.43 rad/s (=23.2rpm) The velocity of the pod is: v2 = ra => v = 12.2 m/s

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