
Since asked for relationship between change in velocity and change in TIME, need to use impulse momentum equations:
- sum F_x = f - m*g*sin(theta). Therefore, integral (f - m*g*sin(theta))*dt = m*v_O2 - m*v_O1
- sum M_O = f*R. Therefore, integral (f*R)*dt = I_O*omega2 - I_O*omega1
KINEMATICS
Need to relate the velocity of O to the omega for the disk. TAKE NO SHORTCUTS HERE!! If you do, you will probably make a sign error. Use the usual rigid body kinematics equation.
Let us know if you have questions.
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