Question 235: Work, Energy and Power & Circular Motion

Question

A particle at rest starts moving with a constant angular acceleration of $4 \mathrm{~rad} / \mathrm{s}^2$ in a circular path. The time at which magnitudes of its centripetal acceleration and tangential acceleration will be equal, is (in second)

Accepted Answer

Given that, $\alpha=4 \mathrm{~rad} / \mathrm{s}^2$
Centripetal (radial) acceleration, $\mathrm{a}_{\mathrm{r}}=\mathrm{r} \omega^2$
Tangential acceleration, $a_t=r \alpha$
If $a_r=a_t$, then $r \omega^2=r \alpha$
$$\begin{array}{ll}
	herefore & \omega^2=\alpha=4 \
	herefore & \omega=\sqrt{4}=2 \mathrm{rad} / \mathrm{s} \
& 	ext { But, } \omega=\omega_0+\alpha \mathrm{t}=0+\alpha \mathrm{t}=\alpha \mathrm{t} \
	herefore & 2=4 \mathrm{t} \
	herefore & \mathrm{t}=\frac{1}{2} \mathrm{~s}
\end{array}$$

Answer

$\frac{1}{4}$

Answer

$\frac{1}{3}$

Answer

$\frac{1}{2}$

Answer

$\frac{2}{3}$

Work, Energy and Power & Circular Motion

A particle at rest starts moving with a constant angular acceleration of 4 \mathrm{~rad} / \mathrm{s}^2 in a circular path. The time at which magnitudes of its centripetal acceleration and tangential acceleration will be equal, is (in second)

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