So I have this problem where I have to calculate circular speed but I don't have the mass. I can only do this by comparison.

So a ball rotates at $2.4 \ ms^{-1}$ with a radius of $0.8$ m. How much would be the velocity if the radius was reduced to $0.48$ m?

How can I do this by only comparing?

I tried calculate Period by doing $\dfrac{2\pi v}{r} = 2.09$ for the first ball but can't pass this.

  • $\begingroup$ Does circular speed means angular velocity ? $\endgroup$ – Bhavay Jun 29 '20 at 23:33
  • $\begingroup$ Well I'm not sure if it is that. Looking at the values I have being v1 = 2.4m/s and r1 = 0.8, and then r2 = 0.48, how much would be v2? $\endgroup$ – lordvader Jun 29 '20 at 23:35
  • $\begingroup$ Hum so v = w.r, I calculate W for v1, and then do the same for v2 and replace w with the value I got from the previous right? $\endgroup$ – lordvader Jun 29 '20 at 23:53
  • $\begingroup$ Yes , physics.stackexchange.com/questions/548631/… u can read this for further understanding. $\endgroup$ – Bhavay Jun 30 '20 at 0:00

I think that one has to assume that there is no torque on the ball about the point it's rotating. So, it is like a pirouette problem \begin{align*} \mathbf{\tau}=\frac{d\mathbf{L}}{dt}=0&\Rightarrow \mathbf{L}\text{ is constant.}\\ \Rightarrow mv_1r_1&=mv_2r_2 \end{align*}


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