Question

A machine part rotates at an angular speed of 0.056 rad/s; its speed is then increased to 1.5 rad/s at an angular acceleration of 0.80 rad/s².

(a) Find the angle through which the part rotates before reaching this final speed.
rad

(b) If both the initial and final angular speeds are doubled and the angular acceleration remains the same, by what factor is the angular displacement changed?

by a factor of 2

by a factor of 4   

by a factor of 16

The angular displacement doesn't change.

Why?

Answer 1

a) given

wi = 0.056 rad/s

wf = 1.5 rad/s

angular acceleration = alpha = 0.8 rad/s^2

from the relation

wf^2-wi^2 = 2**

= wf^2-wi^2/2

= 1.5^2-0.056^2/2*0.8 = 1.4 rad

b) new= (2wf)^2-(2wi^2)/2* = 4*

by a factor of 4