Question

The angular position of a rotating disc is given as $\theta =6t^2+5t-4$ where $\theta$ is in radians, $t$ is in seconds. What is the average angular velocity for the first time interval from $t=0\text{(s)}$ to $t=4\text{(s)}$?

• A. $29\text{rad/s}$
• B. $18\text{rad/s}$
• C. $4\text{rad/s}$
• D. $27\text{rad/s}$

Answer 1

The correct option is A $29\text{rad/s}$

Given,
Angular position $\theta =(6t^2+5t-4)\text{rad}$
Average angular velocity ${\omega }_{\text{avg}}=\frac{\Delta \theta }{\Delta t}$
${\omega }_{\text{avg}}=\frac{{\theta }_f-{\theta }_i}{t_f-t_i}=\frac{\theta (t=4\text{s})-\theta (t=0\text{s})}{4-0}$
Here, $\theta (t=0\text{s})=6\left(0\right)+5\left(0\right)-4$
$=-4\text{rad/s}$
$\theta (t=4\text{s})=6\times (4{)}^2+5\times (4)-4$
$=112\text{rad/s}$
${\omega }_{\text{avg}}=\frac{112-(-4)}{4-0}$
$\therefore {\omega }_{\text{avg}}=29\text{rad/s}$