Question

A wheel starts rotating from rest with constant $\alpha$ and attains an angular velocity of $60$ rad/sec in $5$ seconds. The total angular displacement in radians will be

• A. $60$
• B. $80$
• C. $100$
• D. $150$

Answer 1

The correct option is D $150$

The angular acceleration is given as,

$\alpha =\frac{\omega }{t}$

$=\frac{60}{5}$

$=12rad/s^2$

The angular displacement is given as,

$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

$=0\times t+\frac{1}{2}\times 12\times {\left(5\right)}^2$

$=150rad$

Thus, the total angular displacement is $150rad$.