The angular displacement of a particle is given by $\theta=\omega_0 t+\frac12\alpha t^2$, where $\omega_0$ and $\alpha$ are constants. If $\omega_0=1\,\text{rad/s}$ and $\alpha=1.5\,\text{rad/s}^2$, then at $t=2\,\text{s}$, the angular velocity will be (in rad/s)

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4. Angular velocity is the time derivative of angular displacement. So $\omega=\omega_0+\alpha t=1+1.5\times 2=4\,\text{rad/s}$.

The angular displacement of a particle is given by \(\theta=\omega_0 t+\frac12\alpha t^2\), where \(\omega_0\) and \(\alpha\) are constants. If \(\omega_0=1\,\text{rad/s}\) and \(\alpha=1.5\,\text{rad/s}^2\), then at \(t=2\,\text{s}\), the angular velocity will be (in rad/s)

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