Question

A particle moves from points $1$ to $2$ during a time $\frac{1}{2} s$ . Find the average angular speed of the particle over $\frac{1}{2} s$ ,

$(i)$ in the anticlockwise sense

$(ii)$ in the clockwise sense

Accepted Answer

$(i)$ Let us calculate the change in angular distance $Δϕ$ to find $ω_{av}$ , because we know that the rate of change of angular distance is called angular speed and average angular speed is,

$\frac{1}{2} s$ .

Since,

$Δϕ = ϕ_{2} - ϕ_{1}$ ,

from the diagram,

$ϕ_{2} = + 60 °$ and $ϕ_{1} = - 30 °$

$\Rightarrow Δϕ = (+ 60 °) - (- 30 °) = 90 ° = \frac{π}{2} rad$ .

Hence,

$ω_{av} = \frac{Δϕ}{Δt} = \frac{π / 2}{1 / 2} = π rad s^{- 1}$ .

$(ii)$ If the particle moves from $1$ to $2$ in a clockwise sense, the angular distance,

${Δϕ}^{'} = \frac{3 π}{2} rad$ .
Hence, $ω_{av} = \frac{{Δϕ}^{'}}{Δt} = \frac{3 π / 2}{1 / 2} = 3 π rad s^{- 1}$ .

B M Sharma Solutions for Chapter: Circular Motion, Exercise 4: ILLUSTRATION 9.4

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Circular Motion, Exercise 4: ILLUSTRATION 9.4

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