Calculate the torque, angular momentum and kinetic energy of the water wheels in the table.
[I'll give one example]
High breast water wheel:
Angular velocity/rpm 8
Flow rate*/m3 s−1 1.0
Width or height/m 2.5
Mass/kg 14 143
Power-to-weight ratio/W kg−1 2.8
Torque = Moment of inertia * Angular acceleration
Moment of inertia of thin solid disc = (mr^2)/2 (about z axis)
Angular momentum = Moment of inertia * Angular velocity
Rotational kinetic energy = (Iw^2)/2
The Attempt at a Solution
8rpm -> (8/60)*2*pi rad/s = (4pi)/15 rad/s
Torque = (14143*3.5^2*(angular velocity))/2 = 72572Nm
Angular velocity has here been used instead of angular acceleration due to explanation found here: https://www.physicsforums.com/showthread.php?t=346163
However, this means that the angular momentum calculation gives the same answer (minus a direction, which will take the direction of the angular velocity vector). Have I done this correctly?
Rotational KE = (14143*3.5^2*((4pi)/15)^2)/2 = 60797J
Do these seem at all right?