Answer to Question #128131 in Classical Mechanics for Hassam

Question

A DVD is initially at rest so that the
line PQ on the disc’s surface is along
the +x-axis. The disc begins to turn
with a constant z = 5.0 rad/s2.
At t = 0.40 s, what is the angle
between the line PQ and the +x-axis?

Answer 1

As per the given question,

Initial angular velocity of the disc$(\omega)=0 rad/sec$

Angular acceleration of the disc $(\alpha)=5 rad/sec^2$

angle between the line PQ and x axis=$\theta$

time t=0.4sec

$\theta= \omega t+\frac{\alpha t^2}{2}$

Now, substituting the values,

$\theta = 0+\frac{5\times 0.4^2}{2}$

$\Rightarrow \theta =0.4 radian.$