10. Unbalanced Moments cause Rotational Acceleration

C3 C1 L9 Unbalanced Movements V3

When viewed from above, rotor 1 (on top) spins CW with <span class="mathquill">\omega_1</span>. Rotor 2 (bottom) spins CCW with <span class="mathquill">\omega_2</span>.

When viewed from above, rotor 1 (on top) spins CW with \omega_1. Rotor 2 (bottom) spins CCW with \omega_2.

Look at the "flying car" shown above. It's supported by two rotors spinning in opposite directions. If rotor 1 (top) spins faster than rotor 2, in which direction will the body of the vehicle experience angular acceleration?
SOLUTION: Counter-clockwise (CCW)

Quantity Value
m 1.0
I_z 2.0
k_F 0.1
k_M 0.2
\omega_1 10.0
\omega_2 8.0

Consider a coaxial copter with the above quantities (all values are given in standard units). What will be the resulting linear acceleration \ddot{z}? What about rotational acceleration \ddot{\psi}?

What will the resulting \ddot{z} be for the system described above? Z is positive down.
SOLUTION: -6.6 m/s^2

What will the resulting \ddot{\psi} be for the system described above? CW rotations are positive.
SOLUTION: -3.6 rad/s^2

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