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Question

# A wheel of radius 1 m is performing combined translational and rotational motion on a frictionless horizontal surface with an angular velocity 4 rad/s and translational velocity of its COM is V0=10 m/s as shown in figure. Find the magnitude of velocity of point P, if the line OP makes angle 30∘ with the horizontal.

A
10 m/s
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B
4 m/s
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C
239 m/s
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D
439 m/s
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Solution

## The correct option is C 2√39 m/s Given, Radius of wheel R=1 m Angular velocity of wheel ω=4 rad/s Let velocity at point P=VP Then, −→VP=→V0+→R×→ω Here, V0=10 m/s and Rω=1×4=4 m/s So, |VP|=√(V20)+(Rω)2+2V0(Rω)cosθ Here θ is the angle between V0 & ωR which is 90−30=60∘, so cos60∘=1/2 |VP|=√(10)2+(4)2+2×10×4×1/2 |VP|=2√39 m/s

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