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Question

A wheel is performing combined translational and rotational motion on a frictionless horizontal surface on a truck which is moving with a constant linear velocity v=10 m/s. Centre of the wheel is also moving with a constant linear velocity v=10 m/s with respect to ground. The wheel is rotating with angular velocity ω=2 rad/s. Find velocity of point A with respect to ground. Radius of the wheel is 1 m.



A
10^i
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B
8^i 
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C
6^i 
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D
zero
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Solution

The correct option is A 8^i 
With respect to ground, the wheel is performing (translation + rotational) motion.
Translational velocity of wheel (Vcom)= velocity of truck.
i.e Vcom of wheel =v=10 m/s
As we know,
VA=Vcom+ω×rAO
O is the centre of wheel and A is the highest point on the wheel.
VA=10^i+2(^k)×1(^j)
VA=10^i+2(^i)   [^k×^j=^i]
VA=8^i

Physics

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