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With constant linear velocity, angular velocity of a Gymnast increases :

  • A.By increasing radius
  • B.By decreasing radius
  • C.By increasing radius and velocity
  • D.No change in radius

Answer: B

Angular velocity increases by decreasing the radius.

Linear velocity at the end of a rotating radius is v = rω, so

\[ \omega = \frac{v}{r} \]

With v held constant, a smaller radius gives a larger angular velocity. A gymnast who pulls the body in towards the axis of rotation, for example by tucking, rotates faster.

Increasing the radius lowers ω, so options A and C are wrong (C also changes the velocity, which the question holds constant), and with no change in radius ω stays the same.

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