Question

A solid body starts rotating about a stationary axis with an angular acceleration $alpha$ = $at$. How soon after the beginning of rotation will the total acceleration vector of an arbitrary point of the body form an angle = ${60}^{\circ }$ with its velocity vector?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Total acceleration making ${60}^{\circ }$ with the velocity vector is as good as it making ${60}^{\circ }$ with tangential

acceleration since the direction of both $v$ & $a_t$ is same.

Now from the figure we know

$Tan{60}^{\circ }=\frac{a_N}{a_t}=\sqrt{3}$ .......(i)

$A=a\times t$

Tangential acceleration $a_t=r\alpha =rat$ ........(ii)

Normal acceleration $a_N=\frac{V^2}{R}$

$V=r\omega$

$\Rightarrow a_N=r{\omega }^2$

So we need $\omega$ or $v$

Hmmm................... (we cannot use equations of motion as you know $\alpha$ is variable)

$\alpha$ = $\frac{d\omega }{dt}-at$