Particle `P` shown in figure is moving in a circle of radius `R=10` cm with linear speed `v=2m//s` Find the angular speed of particle about point O.

Options

A. `20 rad s^-1`
B. `10 rad s^-1`
C. `15 rad s^-1`
D. `25 rad s^-1`

Answer

B

Explanation

(b) In a time `t_(P_1 p_2)` particle has moved from to `P_1` to `P_2` (say). `O` is an arbitrary point on the circle (as given in the problem), on its left half.
From the property of a circle. `angleP_2 CP_1 = 2 angleP_2 O P_1`
`omega_C = (angleP_2 CP_1)/(t_(p_1 p_2))` and `omega_0 = (angleP_2 OP_1)/(t_(p_1p_2))`
:. `omega_c = 2 omega_0`
Here `omega_c = (v)/(R) = (200)/(10) = 20 rad s^-1`
:. `omega_0 = 10 rads^-1`.
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