The angular displacement of a rotating body is described by $ heta(t) = \omega_0 t + \frac{1}{2}\alpha t^2$, where $\omega_0 = 1\ ext{rad/s}$ and $\alpha = 1.5\ ext{rad/s}^2$. What is the angular velocity of the body at $t = 2\ ext{s}$?

Question

The angular displacement of a rotating body is described by $	heta(t) = \omega_0 t + \frac{1}{2}\alpha t^2$, where $\omega_0 = 1\ 	ext{rad/s}$ and $\alpha = 1.5\ 	ext{rad/s}^2$. What is the angular velocity of the body at $t = 2\ 	ext{s}$?

Accepted Answer

4 rad/s. Angular velocity is $\omega = \frac{d	heta}{dt} = \omega_0 + \alpha t$. Substituting $\omega_0 = 1$ and $\alpha = 1.5$ at $t=2$ gives $\omega = 1 + 1.5	imes 2 = 4\ 	ext{rad/s}$.

The angular displacement of a rotating body is described by $\theta(t) = \omega_0 t + \frac{1}{2}\alpha t^2$, where $\omega_0 = 1\ \text{rad/s}$ and $\alpha = 1.5\ \text{rad/s}^2$. What is the angular velocity of the body at $t = 2\ \text{s}$?

Solution

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