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Question

As shown in figure, a wheel (r=1 m) is performing combined translational and rotational motion with angular velocity 2 rad/s and the velocity of its centre as VO=4^i m/s. Find the velocity of point B in m/s on the wheel.


A
VB=4^i+2^j
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B
VB=2^i4^j
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C
VB=4^i2^j
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D
VB=2^i+4^j
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Solution

The correct option is C VB=4^i2^j
Angular velocity of ring ω=2^k rad/s, from right hand thumb rule
Velocity of COM of the ring, VO=4^i m/s
For the velocity of point B on ring,
VB=VO+VBO ...(i)
Here,
VBO=ω×rBO ...(ii) rBO=1^i, it represents position vector of B w.r.t centre O.
VBO=(2^k)×(1^i)
VBO=2(^k×^i)=2^j m/s
Substituting in Eq (i),
VB=(4^i2^j) m/s

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