Answer to Question #313957 in Physics for abby

Question

The angular acceleration of a wheel is α = 9.0t⁴ – 5.0t², with α

 in radians per second-squared and t in seconds. At time t = 0, the wheel has an angular velocity of +7 rad/s and an angular position of +5 rad. Write expressions for (a) the angular velocity (rad/s) and (b) the angular position (rad) as functions of time (s).

Answer 1

Given:

$\alpha = 9.0t^4 – 5.0t^2$

$\omega_0=7\:\rm rad/s$

$\theta_0=5\:\rm rad$

(a) the angular velocity

$$\omega=\int \alpha dt+\omega_0=\int (9.0t^4 – 5.0t^2) dt+7\\ =1.8t^5-1.7t^3+7$$

(b) the angular position

$$\theta=\int \omega dt+\theta_0=\int (1.8t^5 – 1.7t^3+7) dt+5\\ =0.3t^6-0.42t^4+7t+5$$