Question

An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θ in time t, through what angle did it rotate in the time ½t?
a. 4θ
b. ¼θ
c. ½θ
d. 2θ
e. θ

Answer 1

Answer:

Angular displacement will be $\frac{1}{4}\Theta$

So option (b) will be the correct option

Explanation:

We have given that firstly object is at rest

So $\omega _i=0rad/sec$

From law of motion we know that angular displacement is given by

$\Theta =\omega _it+\frac{1}{2}\alpha t^2=0\times t+\frac{1}{2}\alpha t^2=\frac{1}{2}\alpha t^2$

Now angular displacement by the object in $\frac{t}{2}sec$

$\Theta =0\times t+\frac{1}{2}\alpha (\frac{t}{2})^2=\frac{1}{4}(\frac{1}{2}\alpha t^2)=\frac{1}{4}\Theta$

So option (b) will be the correct option