Question

A machine part rotates at an angular speed of 0.76 rad/s; its speed is then increased to 2.96 rad/s using an angular acceleration of 1 rad/s 2 . Find the angle through which the part rotates before reaching this final speed. Answer in units of rad.

Answer 1

Answer:

θ = 4.092 °

Explanation:

Given that

Initial Angular speed ,ωi = 0.76 rad/s

Final angular speed ,ωf= 2.96 rad/s

The angular acceleration ,α = 1 rad/s²

We know that

ωf² = ωi ²+ 2 α θ

θ=Angle rotates

2.96² = 0.76²+ 2 x 1 x θ

$\theta=\dfrac{2.96^2-0.76^2}{2}\ degrees\\\theta=4.092\ degrees$

Therefore the angle rotates by machine part will be 4.092 degrees.

θ = 4.092 °