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Question

If two particles are moving on same circle with different angular velocities ω1 and ω2, and different time periods T1 and T2, then the time taken by the particle 2 to complete one revolution with respect to particle 1 is

A
T=T1T2T2T1
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B
T=T1+T22
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C
T=T1T2T2+T1
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D
T=T2T1
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Solution

The correct option is C T=T1T2T2+T1
Case-(i): Both moving in same direction
Relative angular velocity is given by ω2ω1
T=2πω2ω1
=2π2πT22πT1
=T1T2T1T2
Case-(ii): Both moving in opposite direction.
Relative angular velocity is given by
ω2+ω1
T=2πω2+ω1
=2π2πT2+2πT1
=T1T2T1+T2

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