Any questions??
Discussion and hints:
It is RECOMMENDED that you choose to put your observer on the disk. In that case, the ω and α that go into your acceleration equation will be that of the disk. And, the observer will see no motion of point A, which results in the v_rel and a_rel terms of that equation being zero.
The discussion below follows a choice of putting the observer on the disk.
The disk shown above has TWO components of rotation:
- a rotation rate of ω0 about a fixed axis (the “-” Z-axis), and,
- a rotation rate of ωdisk about a moving axis (the “+” y-axis)
(Be sure to make a clear distinction between the lower case and upper case symbols.)
Therefore, the angular velocity of the disk is given by:
ω = -ω0K + ωdisk j
The angular acceleration vector α is simply the time derivative of the angular velocity vector ω : α = dω/dt. In taking this time derivative,
- Recall that the K-axis is fixed. Since K is fixed, then dK/dt = 0.
- Recall that the j-axis is NOT fixed. Knowing that, how do you find dj/dt?