Question

A disc starts from rest and on the application of a torque, it gains an angular acceleration given by α = 3t-t². Calculate the angular velocity after 2 s.

Answer 1

10/3 rad/s

Answer 2

1. Recognize that angular acceleration is the derivative of angular velocity with respect to time ($\alpha = d\omega/dt$).
2. Integrate the given $\alpha(t)$ with respect to time to find $\omega(t)$.
3. Use the initial condition ($\omega=0$ at $t=0$) to determine the integration constant.
4. Substitute $t=2$ s into the derived $\omega(t)$ expression.

The angular velocity after 2 s is $\frac{10}{3}$ rad/s.