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Question
Consider a wheel of a bicycle rolling on a level road at a linear speed \[\nu_0\] (see the following figure)
(a) the speed of the particle A is zero
(b) the speed of B, C and D are all equal to \[v_0\]
(c) the speed of C is 2 \[v_0\]
(d) the speed of B is greater than the speed of O.
Solution
(a) the speed of the particle A is zero
(c) the speed of C is 2 \[v_0\]
(d) the speed of B is greater than the speed of O
For pure rolling,
\[\omega r = v_0\]
Velocity of the particle at A, B, C and D will be resultant of v0 and ωr.
At point B,
\[v_{net} = \sqrt{{v_0}^2 + \left( \omega r \right)^2}\]
\[ v_{net} = \sqrt{{v_0}^2 + {v_0}^2}\]
\[ v_{net} = \sqrt{2} v_0\]
At point C,
\[v_{net} = v_0 + \left( \omega r \right)\]
\[ v_{net} = 2 v_0\]
At point A,
\[v_{net} = v_0 - \left( \omega r \right)\]
\[ v_{net} = 0\]
At point O,
r = 0
\[\therefore v_{net} = v_0\]
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