First slide

Angular velocity, Angular acceleration

Question

A particle starts from rest and moves along a circular path of radius 5m with a tangential acceleration of constant magnitude. If the length of path traversed by the particle in 2 second is 20 m, its angular acceleration is

Easy

A

2.5 $r a d / \sec^{2}$
B

0.75 $r a d / \sec^{2}$
C

1.5 $r a d / \sec^{2}$
D

2 $r a d / \sec^{2}$

Solution

If $a_{t}$ be the tangential acceleration of the particle, than $S = \frac{1}{2} a_{t} . t^{2} \Rightarrow a_{t} = \frac{2 s}{t^{2}}$
$∴ α = \frac{a_{t}}{r} = \frac{2 S}{r t^{2}} = \frac{2 \times 20}{5 \times 2^{2}} r a d / s^{2} = 2 r a d / \sec^{2}$

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