First slide

Rolling motion

Question

A cotton reel rolls without sliding such that the point P of the string has velocity v = 6 m/s. If r = 10 cm and R = 20 cm, then the velocity of its centre C is

Difficult

A

$2.5 m / s$
B

$5 m / s$
C

$4 m / s$
D

$2 m / s$

Solution

As cotton reel rolls point of contact of reel with ground will act as instantaneous axis of rotation.
$\begin{array}{l} v_{p} = ω (R + r) \\ \Rightarrow ω = \frac{v_{p}}{R + r} = 20 rad / s \end{array}$
Velocity of centre of reel
$v_{C} = ω R = \frac{v_{p} R}{(R + r)} = \frac{6 \times 20}{(20 + 10)} = 4 m / s$

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