Question

A particle is moving with a constant angular acceleration of $4rad/s^2$ in a circular path. At time $t=0$, particle was at rest. Find the time at which the magnitudes of centripetal acceleration and tangential acceleration are equal.

• A. $\frac{1}{2}s$
• B. $1s$
• C. $\frac{3}{2}s$
• D. $2s$

Answer 1

The correct option is A $\frac{1}{2}s$

Initial angular velocity of the particle $w_i=0$

Angular acceleration $\alpha =4rad/s^2$

Using $w=w_i+\alpha t$

$\therefore$ $w=0+\alpha t$ $⟹w=\alpha t$

Thus radial acceleration $a_r=r{w}^2=r{\alpha }^2{t}^2$ ...........(1)

Also tangential acceleration $a_t=r\alpha$ ........(2)

Equating (1) and (2) we get $r{\alpha }^2{t}^2=r\alpha$

$\therefore$ $t^2=\frac{1}{\alpha }=\frac{1}{4}$ $⟹t=0.5$ s