Question

During a 7.0-s time interval, a flywheel with a constant angular acceleration turns through 600 radians that acquire an angular velocity of 100 rad/s.

1. The angular velocity at the beginning of the 7.0s is _________
2. The angular acceleration of the flywheel is ________

Answer 1

1. By definition, the angular acceleration is:

$$\varepsilon =\dfrac{\Delta \omega }{\Delta t}$$

where $\Delta \omega = 100 rad/s$ is the gain in angular velocity in time interval $\Delta t = 7s$. Thus, obtain:

$$\varepsilon = \dfrac{100rad/s}{7s}\approx 14.3\space rad/s^2$$

2. The number of radians the wheel turned throug is given as follows:

$$\varphi = \omega_0(\Delta t) + \dfrac{\varepsilon(\Delta t)^2}{2}$$

where $\omega _0$ is the initial angular velocity. Substituting the expression for $\varepsilon$ and $\varphi = 600rad$ and expressing $\omega_0$, obtain:

$$\omega_0 = \dfrac{\varphi}{\Delta t}-\dfrac{\Delta \omega }{2}\\ \omega_0 = \dfrac{600rad}{7s}-\dfrac{100rad/s}{2} \approx 35.7\space rad/s$$

Answer. 1) 35.7 rad/s, 2) 14.3 rad/s^2.