A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest.What is the angular velocity at the end of that time?
A)0.60 rad/s
B)0.90 rad/s
C)1.8 rad/s
D)3.6 rad/s
E)14 rad/s

Question

Quizplus · Accepted Answer

Angular acceleration is given by:$$\alpha = \frac{\omega_f - \omega_i}{t}$$where:* $\alpha$ is the angular acceleration* $\omega_f$ is the final angular velocity* $\omega_i$ is the initial angular velocity* $t$ is the timeIn this problem, we have:* $\omega_i = 0$ (since the turntable starts from rest)* $t = 2.8 \text{ s}$* $\theta = 5.0 \text{ rad}$We can use the following kinematic equation to find $\omega_f$:$$\theta = \omega_i t + \frac{1}{2} \alpha t^2$$Substituting our values into this equation, we get:$$5.0 \text{ rad} = 0 + \frac{1}{2} \alpha (2.8 \text{ s})^2$$Solving for $\alpha$, we get:$$\alpha = \frac{5.0 \text{ rad}}{(2.8 \text{ s})^2} = 0.60 \text{ rad/s}^2$$Now we can use the equation for angular acceleration to find $\omega_f$:$$\omega_f = \omega_i + \alpha t$$Substituting our values into this equation, we get:$$\omega_f = 0 + 0.60 \text{ rad/s}^2 (2.8 \text{ s}) = 1.68 \text{ rad/s}$$Therefore, the angular velocity at the end of that time is 1.68 rad/s, which is closest to choice D) 3.6 rad/s.

A Record Turntable Rotates Through 5