Question

An object starts from rest and accelerates at a rate of 2 rad/s^2 until it reaches an angular speed of 24 rad/s. The object then accelerates at a rate of -3 rad/s2 until it stops. Through what angular displacement (in rad) does the object move between when it starts moving and when it stops?

Answer 1

Answer:

Total angular displacement will be 240 radian

Explanation:

In first case object starts from rest so initial angular speed $\omega _i=0rad/sec$

Angular acceleration is given $\alpha =2rad/sec^2$

Final angular speed$\omega _f=24rad/sec$

From third equation of motion $\omega _f^2=\omega _i^2+2\alpha \Theta$

So $24^2=0^2+2\times 2\times \Theta$

$\Theta =144$ radian

Now in second case as the objects finally stops

So final velocity $\omega _f=0rad/sec$

Angular acceleration $\alpha =-3rad/sec^2$

So $0^2=24^2-2\times 3\times \Theta$

$\Theta =96$ radian

So total angular displacement will be 96+144 = 240 radian