The angular momentum of a flywheel

[Eggyu]

The angular momentum of a flywheel having a rotational inertia of 0.200 kg·m2 about its axis decreases from 3.00 to 1.800 kg·m2/s in 1.80 s.

(a) What is the average torque acting on the flywheel about its central axis during this period?
N·m
(b) Assuming a uniform angular acceleration, through what angle will the flywheel have turned?
rad
(c) How much work was done on the wheel?
J
(d) What is the average power of the flywheel?
W

Basically, all i need is how to find the initial angular velocity for part b. The rest of the variables i have solved for.

 

[andrevdh]

The angular momentum of a rigid object about a fixed axis is given by

$$L = I\omega$$

where $$I$$ is its moment of inertia bout this axis and $$\omega$$ is its angular speed about the same axis.

 

[Bill Foster]

The rotational components and equations are analogous to linear ones.

Equation of motion:

linear:
(1) $$x=x_0+vt+\frac{1}{2}at^2$$
(2) $$v=v_0+at$$
(3) $$F=ma$$
(4) $$W=Fx$$
(5) $$P=Fv$$
(6) $$a(x-x_0)=\frac{1}{2}(v^2-v_0^2)$$

angular:

(1) $$\phi=\phi_0+\omega t+\frac{1}{2}\alpha t^2$$
(2) $$\omega=\omega_0+\alpha t$$
(3) $$\tau=I\alpha$$
(4) $$W=\tau \phi$$
(5) $$P=\tau \omega$$
(6) $$\alpha(\phi-\phi_0)=\frac{1}{2}(\omega^2-\omega_0^2)$$

So to find the average torque in part (a), find the deceleration using angular equation 2.

Part (b), use 6.

Part (c), use 4.

Part (d), use 5.