Question

Your electric drill rotates initially at 5.21 rad/s. You slide the speed control and cause the drill to undergo constant angular acceleration of 0.311 rad/s2 for 4.13 s. What is the drill's angular displacement during that time interval?

Answer 1

The drill's angular displacement during that time interval is 24.17 rad.

Step-by-step explanation:

Given;

initial angular velocity of the electric drill,
`\omega _i` = 5.21 rad/s

angular acceleration of the electric drill, α = 0.311 rad/s²

time of motion of the electric drill, t = 4.13 s

The angular displacement of the electric drill at the given time interval is calculated as;

`\theta = \omega _i t \ + \ (1)/(2)\alpha t^2\\\\\theta = (5.21 \ * \ 4.13) \ + \ (1)/(2)(0.311)(4.13)^2\\\\\theta = (21.5173 ) \ + \ (2.6524)\\\\\theta =24.17 \ rad`

Therefore, the drill's angular displacement during that time interval is 24.17 rad.