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

Step-by-step 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* \alpha * \theta`

where
`\theta`=angle turned by drill

`\omega _0`=initial angular velocity

`\omega`=final angular velocity

`\alpha`=angular acceleration

`\omega ^2-0=2* \alpha * \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 * 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 =(\omega ^2)/(2\alpha )`

`\theta =1\ rad`