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Question

When a person throws a meter stick, it is found that the centre of the stick is moving with a speed of 10 m/s vertically upward & the left end of the stick with a speed 20 m/s vertically upward. Then, the angular speed of the stick is

A
20 rad/sec
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B
10 rad/sec
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C
30 rad/sec
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D
None of the these
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Solution

The correct option is A 20 rad/sec

Assume angular velocity of the stick is ω rad/s in clockwise direction.
For meter stick, L=1 m
Speed of left end of the stick VA=20 m/s
As we know,
VA=V0+ω×rAO {rAO=12^i}
20^j=10^j+ω(^^k)×12(^i)
10^j=ω2(^k×^i)[^k×^i=^j]
10^j=ω2^j
ω=20 rad/s
[ω is positive hence, assumed direction is correct.]

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