Amachine part rotates at an angular speed of 0.07 rad/s; its speed is then increased to 3.4 rad/s at an angular acceleration of 0.50 rad/s2. (a) find the angle through which the part rotates before reaching this final speed. 11.5 correct: your answer is correct. rad (b) in general, if both the initial and final angular speed are doubled at the same angular acceleration, by what factor is the angular displacement changed? why?

In first case angular displacement will be 11.55 radian

In second case it will be 4 times the previous case          

Explanation:

We have given that machine rotates at an angular velocity of 0.07 rad/sec

So initial angular velocity

And its speed is increases to 3.4 rad/sec

So final angular velocity is

Angular acceleration

According to third equation of motion we know that

Now initial angular velocity and final angular velocity both are doubled but angular acceleration is constant

So

And  

So

So angular displacement will be 4 times the earlier displacement  

inverse v=i*r

nice nice