Question

A machine 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?

Answer 1

Answer:

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 $\omega _i=0.07rad/sec$

And its speed is increases to 3.4 rad/sec

So final angular velocity is $\omega _f=3.4rad/sec$

Angular acceleration $\alpha =0.5rad/sec^2$

According to third equation of motion we know that

$\omega _f^2=\omega _i^2+2\alpha \Theta$

$3.4^2=0.07^2+2\times 0.5\times \Theta$

$\Theta =11.55radian$

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

So $\omega _i=2\times 0.07=0.14rad/sec$

And  $\omega _f=2\times 3.4=6.8rad/sec$

So $6.8^2=0.14^2+2\times 0.5\times \Theta$

$\Theta =46.22radian$

So angular displacement will be 4 times the earlier displacement