First slide

Rotational motion

Question

A uniform disc of mass M and radius R is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward
pull T is exerted on the cord. The angular acceleration of the disc is

Easy

A

$\frac{T}{M R}$
B

$\frac{M R}{T}$
C

$\frac{2 T}{M R}$
D

$\frac{M R}{2 T}$

Solution

Torque exerted on the disc
$τ = T R N o w τ = I α \begin{array}{l} α = \frac{τ}{I} = \frac{T R}{\frac{1}{2} M R^{2}} \\ = \frac{2 T R}{M R^{2}} = \frac{2 T}{M R} \end{array}$

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