Question

A flywheel at rest is to reach an angular velocity of 24 rad/s in 8 second with constant angular acceleration. The total angle turned through during this interval is

• A. 24 rad
• B. 48 rad
• C. 72 rad
• D. 96 rad

Answer 1

Answer: (D)

96 rad

Answer 2

To determine the total angle turned through by a flywheel starting from rest and reaching an angular velocity of 24 rad/s in 8 seconds with constant angular acceleration, we can use the kinematic equations for rotational motion.
Given:
- Initial angular velocity, $\omega_0 = 0$ rad/s (since it starts from rest)
- Final angular velocity, $\omega = 24$ rad/s
- Time, $t = 8$ seconds
First, we need to find the angular acceleration $\alpha$. Using the kinematic equation for angular velocity:
$\omega = \omega_0 + \alpha t$
Solving for $\alpha$:
$24 = 0 + \alpha \cdot 8$
$\alpha = \frac{24}{8} = 3 \text{ rad/s}^2$
Now, to find the total angle $\theta$ turned through, we use the kinematic equation for angular displacement:
$\theta = \omega_0 t + \frac{1}{2} \alpha t^2$
Substituting the known values:
$\theta = 0 \cdot 8 + \frac{1}{2} \cdot 3 \cdot (8)^2$
$\theta = \frac{1}{2} \cdot 3 \cdot 64$
$\theta = \frac{3 \cdot 64}{2}$
$\theta = \frac{192}{2}$
$\theta = 96 \text{ radians}$
Thus, the total angle turned through by the flywheel during this interval is option (D) $\boxed{96 \text{ radians}}$.