Question

If two bodies in circular paths of radii 1: 2 take same time to complete their

circles, what is the ratio of their angular speeds?
pls help.

Answer 1

I hope the ratio of sped is 1:2
According to me
Angular veocity or speed=angular displacement/time
So angular displacement is circular path and their path is diameter so the formula of diameter is 2*pie*radius
So both ratio are 2*pie*1/T /2*pie*2/T
2*pie will cancel out and T is a same so it also cancel out the the left ratio is 1:2.
Thank you

Answer 2

Answer:

Ratio of angular speeds is = 1 : 2

Explanation:

Suppose the common factor of the ratio is 'l'. The radii will be l and 2l.

Now the formula for angular speed is: ω = $\frac{v}{r}$, where 'v' is the speed and 'r' is the radius.

• Angular speed of 1st body: 1st body is moving around a circular path of radius = l. The distance = 2πl and time taken = t.

      speed = v = $\frac{2\pi l}{t}$   and angular velocity = ω = $\frac{v}{r}$ = $\frac{\frac{2\pi l}{t}}{l}$ = $\frac{2\pi }{t}$

• Angular speed of 2nd body: 1st body is moving around a circular path of radius = 2l. The distance = 2π(2l) = 4πl and time taken = t.

       speed =  v = $\frac{4\pi l}{t}$   and angular velocity = ω' = $\frac{v}{r}$ = $\frac{\frac{4\pi l}{t}}{2l}$ = $\frac{4\pi }{t}$

• Ratio: Ratio of angular speeds = ω : ω'

                                                           =  $\frac{2\pi }{t}$ : $\frac{4\pi }{t}$

                                                           = 1 : 2

         

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