In general, kinetic energy for planar motion of a rigid body is given by: T = (1/2)*m*v_A^2 + (1/2)*I_A*omega^2
where A is either the cm or a fixed point.
- In Problem 6/116, the crate is in pure rotation about point O after the cable is cut. Therefore, use A = O and the final KE is given by T2 = (1/2)*I_O*omega_2^2. Note that you will need to use the P.A.T. to find the mass moment of inertia about point O (the mass moment of inertia for a rectangular body about the cm is given in the appendix of the textbook).
- In Problem 6/118, the log is in pure translation (log remains horizontal for all positions -- constant angle, zero angular velocity). Suggest that you use A = G (cm of log), and therefore the final KE is given by T2 = (1/2)*m*v_G^2. That is, the log moves as a particle.
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