Question 295: 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. At what time the magnitude of its centripetal acceleration and tangential acceleration will be equal?

Accepted Answer

$$\alpha=4 \mathrm{~rad} / \mathrm{s}^2$$
Centripatal ( radial) acceleration, $$a_{\mathrm{r}}=r \omega^2$$
Tangential acceleration, $$a_t=r \alpha$$
If $$\mathrm{a}_{\mathrm{r}}=\mathrm{a}_{\mathrm{t}}$$, then $$\mathrm{r} \omega^2=\mathrm{r} \alpha$$
$$\begin{aligned}
&	herefore \quad \omega^2=\alpha=4 \
& \quad \omega=\sqrt{4}=2 \mathrm{rad} / \mathrm{s} \
& \omega=\omega_0=\alpha \mathrm{t} \quad=0+\alpha \mathrm{t}=\alpha \mathrm{t} \
& 	herefore 2=4 \mathrm{t} \
& 	ext { or } \mathrm{t}=\frac{1}{2} \mathrm{~s}
\end{aligned}$$

Answer

$$\frac{1}{4} \mathrm{~S}$$

Answer

$$\frac{2}{3} \mathrm{~S}$$

Answer

$$\frac{1}{2} \mathrm{~S}$$

Answer

$$\frac{1}{3} \mathrm{~S}$$

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. At what time the magnitude of its centripetal acceleration and tangential acceleration will be equal?

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