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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 (Which is the topmost point of wheel as shown in the figure) 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 B 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

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