Question 274: 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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