A particle starting from rest, moves in a circle of radius $r$. It attains an angular velocity of $\

Question

A particle starting from rest, moves in a circle of radius $r$. It attains an angular velocity of $\omega_{0} \mathrm{~rad} / \mathrm{s}$ in the $n^{	ext {th }}$ round. Its tangential acceleration will be

Professor PC Thomas Classes · Answer

(a): Angular displacement in $n$ rounds $= 2 \pi n \mathrm{~rad}$. \ Using $\omega^{2}=\omega_{u}^{2}+2 \alpha 	heta \Rightarrow \omega_{0}^{2}=0+2 \alpha(2 \pi n) \Rightarrow \alpha=\frac{\omega_{0}^{2}}{4 \pi n}$. \ Tangential acceleration, $a_{t}=r \alpha=\frac{\omega_{0}^{2} r}{4 \pi n} \mathrm{~m} / \mathrm{s}^{2}$