First slide

Rolling motion

Question

A ring is rolling on a rough horizontal surface without slipping with a linear speed v. Referring to Figure linear speed of point X is:

Moderate

A

$vsin θ$
B

v
C

$2 vcos \frac{θ}{2}$
D

$2 vsin \frac{θ}{2}$

Solution

Here point O is IC₁ and OX $= 2 Rsin \frac{θ}{2}$
So, $v_{X} = ω (2 Rsin θ / 2)$
$\Rightarrow v_{X} = 2 vsin \frac{θ}{2}$

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