Question

A wheel rotates with a constant angular acceleration of 3.50 rad/s². If the angular speed of the wheel is 2.00rad/s at t1=0,
(a) through what angle does the wheel rotate in 2.00 s?
(b) what is the angular speed at t = 2.00 s?

Answer 1

A wheel rotates with a constant angular acceleration of $3.50 \, \text{rad/s}^2$. If the angular speed of the wheel is $2.00 \, \text{rad/s}$ at $t1 = 0$,

(a) through what angle does the wheel rotate in 2.00 s?

(b) what is the angular speed at $t = 2.00$ s?

A wheel will rotate at angle:

$$\varphi = \omega_0 t + \frac{\beta t^2}{2}$$

Where $\beta$ - angular acceleration

$$\varphi = 2 \, \text{rad/s} \times 2 \, \text{s} + \frac{3.5 \, \text{rad/s}^2 \times (2 \, \text{s})^2}{2} = 11 \, \text{rad}$$

Angular speed:

$$\omega = \omega_0 + \beta t$$ $$\omega = 2 \, \text{rad/s} + 3.5 \, \text{rad/s}^2 \times 2 \, \text{s} = 9 \, \text{rad/s}$$

Answer: $\varphi = 11 \, \text{rad}, \omega = 9 \, \text{rad/s}$