Question

A wheel rotates about a fixed axis with an initial angular velocity of 24 rad/s. During a 4 s interval the angular velocity decreases to 14 rad/s. Assume that the angular acceleration is constant during the 4 s interval. How many radians does the wheel turn through during the 4 s interval

Answer 1

Answer:

$\theta=76\ rad$

Explanation:

Hoven that,

Initial angular velocity of the wheel = 24 rad/s

Final angular velocity = 14 m/s

Time, t = 4 s

We need to find how many radians does the wheel turn through during the 4 s interval. Let the displacement is $\theta$. Using second equation of rotational kinematics to find it such that,

$\theta=\omega_i t+\dfrac{1}{2}\alpha t^2$

Where

$\alpha$ is angular acceleration

$\alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{14-24}{4}\\\\\alpha =-2.5\ rad/s^2$

So,

$\theta=24\times 4+\dfrac{1}{2}\times (-2.5)\times 4^2\\\\\theta=76\ rad$

So, it will turn 76 radian during the 4 s interval.