First slide

The two types of acceleration

Question

A particle travels in a circle of radius 20 cm at a uniformly increasing speed. If the speed changes from 8 ${ms}^{- 1}$ to 9 ${ms}^{- 1}$ in 2s, what would be the angular acceleration (in rad $s^{- 2}$ )? [UK PMT 2015]

Easy

A

1.5 rad $s^{- 2}$
B

2.5 rad $s^{- 2}$
C

3.5 rad $s^{- 2}$
D

4.5 rad $s^{- 2}$

Solution

Given, radius of the circle $= 20 cm = 20 \times 10^{- 2} m$
When speeds are 8 ${ms}^{- 1}$ and 9 ${ms}^{- 1}$ then angular speeds are
respectiveIy, $ω_{1} = \frac{8}{20 \times 10^{- 2}} = 40 {rads}^{- 1}$
and $ω_{2} = \frac{9}{20 \times 10^{- 2}} = 45 {rads}^{- 1}$
$∴$ Angular acceleration $= \frac{ω_{2} - ω_{1}}{t} = \frac{45 - 40}{2} = 2.5 {rads}^{- 2}$

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