Question 267: Work, Energy and Power & Circular Motion

Question

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?

Accepted Answer

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

Answer

0.4 s

Answer

0.5 s

Answer

0.8 s

Answer

1.0 s

Work, Energy and Power & Circular Motion

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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