A particle at rest starts moving with constant angular acceleration $4 \mathrm{rad} / \mathrm{s}^2$ in circular path. At what time the magnitudes of its tangential acceleration and centrifugal acceleration will be equal?

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Aicharya · Accepted Answer

In rotational motion, $\begin{aligned} & \omega=\omega_0+\alpha \mathrm{t} \ & \omega=\alpha \mathrm{t} \end{aligned}$ $	ext { ( } \because \omega_0=0 	ext {; particle at rest.) }$ $	herefore \quad$ Centrifugal acceleration $\mathrm{a}=\omega^2 \mathrm{r}$ $	herefore \quad \mathrm{a}=\alpha^2 \mathrm{t}^2 \mathrm{r}$ Tangential acceleration $\mathrm{a}_{\mathrm{t}}=\alpha 	imes \mathrm{r}$ Given: $\mathrm{a}=\mathrm{a}_{\mathrm{t}}$ $\Rightarrow \alpha^2 \mathrm{t}^2 \mathrm{r}=\alpha \mathrm{r}$ $\mathrm{t}^2=\frac{1}{\alpha}=\frac{1}{4}$ $	herefore \quad \mathrm{t}=\frac{1}{2}=0.5 \mathrm{~s}$

A particle at rest starts moving with constant angular acceleration $4 \mathrm{rad} / \mathrm{s}^2$ in…

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