Question

If two particles are moving on same circle or different circles in same plane with different angular velocities w1 and w2 and different time period T1 and T2 in same sense,then the time taken by 2 to complete one revolution w.r.t particle 1 is

Answer 1

Answer:

                 $T = T_{1}T_{2} /(T_{1}-T_{2} )$

Explanation:

If $w_{1} ,w_{2}$  are angular velocity of the particles and $T_{1} ,T_{2}$   are time taken by them.

Hence,$T_{1} =\frac{2\pi }{w_{1} },T_{2}=\frac{2\pi }{w_{2} }$ are individual time taken.

Then relative time taken $T =\frac{2\pi }{w_{relative} }$

$w_{relative} =w_{2}-w_{1}$

Hence,relative time,$T_{relative} =\frac{2\pi }{w_{2}-w_{1}  }$

So, $T = T_{1}T_{2} /(T_{1}-T_{2} )$

Where t is relative time.