Question

A wheel has a constant angular acceleration of $3rad/s{}^2$. During a $4s$ interval, it turns through an angle of $60$ rad. If the wheel started from rest, how long has it been in motion before the start of this $4s$ interval?

• A. $3s$
• B. $6s$
• C. $9s$
• D. $12s$

Answer 1

The correct option is A $3s$

Angular acceleration $\alpha =3rad/s^2$

From rotational kinematics:

$\theta ={\omega }_{1}t+\frac{1}{2}\alpha t^2$ [during the $4s$ internal]

$60=4{\omega }_1+\frac{1}{2}\times 3\times 16=4w_1+244{\omega }_1=36{\omega }_1=9rad/s$

The wheel starts from res, therefore ${\omega }_0=0$

${\omega }_1={\omega }_0+\alpha t^{{}^{\prime }}9=0+3t^{{}^{\prime }}{t}^{{}^{\prime }}=\frac{9}{3}=3s$