Question

An electric drill starts from rest and rotates with a constant angular acceleration. After the drill has rotated through a certain angle, the magnitude of the centripetal acceleration of a point on the drill is twice the magnitude of the tangential acceleration. What is the angle?

Answer 1

Answer:

Explanation:

Given

magnitude of centripetal acceleration is twice the magnitude of tangential acceleration

Suppose $\theta$ is theta angle rotated by electric drill

it is given that it starts from rest i.e. $\omega _0=0$

suppose $\omega$ and $\alpha$ is the final angular velocity and angular acceleration

using rotational motion equation

$\omega ^2-\omega _0^2=2\times \alpha \times \theta$

where $\theta$=angle turned by drill

$\omega _0$=initial angular velocity

$\omega$=final angular velocity

$\alpha$=angular acceleration

$\omega ^2-0=2\times \alpha \times \theta$

$\omega ^2=2\alpha \theta ---1$

It is also given that centripetal acceleration is twice the magnitude of tangential i.e.

$\omega ^2r=\alpha \times r$

where r=radial distance of any point from axis of drill

i.e. $\omega ^2=\alpha$

substitute this value to equation 1

we get

$\theta =\frac{\omega ^2}{2\alpha }$

$\theta =1\ rad$