The following image shows a circular disk rolling on a surface. If the velocity of a point on the edge of the circular disk is $V{p}$ and the velocity of the center of the disk is $V_{cm}$ then find $\frac{V_p}{V_{cm}}$.
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user258250
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Are you asking the ratio of magnitude of velocities? – Aditya Agarwal Aug 15 '15 at 04:53
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@AdityaAgarwal Yes. – user258250 Aug 15 '15 at 11:27
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$$\frac{V_p}{V_{cm}}=2$$ It holds true because from the rule of addition of velocities in classical mechanics follows that $V_p=V_{cm}+v$, where $v=\omega r \rightarrow v=\frac{2\pi r}{T}$ and $V_{cm}=\frac{2\pi r}{T} \rightarrow V_p=2V_{cm}$.
Note that the velocity of the point of touching the ground equals zero, because we have a sum of two velocities with the same value like at the top point, but with exactly opposite directions.
blitzar787
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According to an equation that i recently found, this ratio of velocities occur when the point is exactly at the highest point and zero when the point is in contact with the surface. – user258250 Aug 15 '15 at 04:00
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But velocity and speed have a ton of differences between them. Velocity is vector and speed is scalar. Velocity is displacement by time, speed is speed by time. So if we erase the term velocity, and I ask what will be the ratio of speed then? – Aditya Agarwal Aug 15 '15 at 05:20
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It would be $1$. I don't think you can calculate the ratio of velocity without vectors? – Aditya Agarwal Aug 15 '15 at 05:21
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@AdityaAgarwal Did you find any discription of vectors here. The speed ratio while the point is at the topmost point is also 2. – user258250 Aug 15 '15 at 05:23