Question

A grindstone starts from rest and has a constant-angular acceleration of $4.0rad/se{c}^2$. The angular displacement and angular velocity, after $4sec$ will respectively be

• A. $32rad,64rad/sec$
• B. $32rad,16rad/sec$
  
• C. $16rad,32rad/sec$
• D. $64rad,32rad/sec$

Answer 1

The correct option is B $32rad,16rad/sec$


Given,
$\alpha =4.0rad/se{c}^2$
Angular displacement after $4sec$ is,
$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$
$=\frac{1}{2}\alpha t^2=\frac{1}{2}\times 4\times 4^2=32rad$
Angular velocity after $4sec$
$\omega ={\omega }_0+at$
$=0+4\times 4=16rad/sec$

Final Answer: (a)