Answer to Question #162637 in Physics for An

Question

A flywheel with a diameter of 1.0 m and initially rotating at 500 rpm, rotate at 1000 rpm after 20 s. Assuming a constant angular acceleration,

a. find the value of the angular acceleration.

b. find the angle through which the flywheel turns in moving from 500 rpm to 1000 rpm.

c.find the acceleration of any point on the rim.

Answer 1

a)

$$\alpha=\dfrac{\omega_f-\omega_i}{t},$$

$\alpha=\dfrac{1000\ \dfrac{rev}{min}\cdot\dfrac{1\ min}{60\ s}\cdot2\pi\ rad-500\ \dfrac{rev}{min}\cdot\dfrac{1\ min}{60\ s}\cdot2\pi\ rad}{20\ s}=2.62\ \dfrac{rad}{s^2}.$

b)

$$\theta=\omega_0t+\dfrac{1}{2}\alpha t^2,$$

$\theta=500\ \dfrac{rev}{min}\cdot\dfrac{1\ min}{60\ s}\cdot2\pi\ rad\cdot20\ s+\dfrac{1}{2}\cdot2.62\ \dfrac{rad}{s^2}\cdot(20\ s)^2=1571.2\ rad.$

c)

$$a=r\alpha=0.5\ m\cdot2.62\ \dfrac{rad}{s^2}=1.31\ \dfrac{m}{s^2}.$$