Answer to Question #287289 in Physics for Hana

Question

1. A flywheel, in the form of uniform disk, is 4.0 m in diameter and weighs 637 N. What will be its angular acceleration if it is activated upon by net torque of 225J?

2. When you switch your room fan from medium to high speed, the blades accelerate at 1.2 radians per second squared for 1.5 seconds. If the initial angular speed of the fan blades is 3.0 radians per second, what is the final angular speed of the fan blades in radians per second?

(Show the solution if it's ok with you, thank you)

Answer 1

1. The angular acceleration:

$$\alpha=\dfrac\tau I=\dfrac\tau{\frac12mR^2}=\dfrac\tau{\frac12\frac WgR^2}=\dfrac{8g\tau}{WD^2},\\\space\\ \alpha=1.73\text{ rad/s}^2.$$

2. The final angular speed:

$$\omega_2=\omega_1+\alpha t=4.8\text{ rad/s}.$$