physics rotational work and energy problem?

Question

three objects lie in the x, y plane. each rotates about the z axis with an angular speed of 6.00 rad/s. the mass (m) of each object and its perpendicular distance (r) from the z axis are as follows: (1) m1= 6.00 kg and r1= 2.00m, (2) m2= 4.00kg and r2=1.50m, (3) m3= 3.00kg and r3= 3.00m.

(a) find the tangential speed of each object.
(b) determine the totale kinectic engery of this system
(c) obtain the moment of inertia of the system
(d) find the rotational kinetic energy of the system

confused..anyone know who to work this?

Answer 1

1. the tangential speed of each is radius times angular velocity, both are given.

2. It seems like the question is asking you to calculate the sum of KE for each mass where v is the tangential speed calculated in step one. Sum of 1/2mv^2 for 3 masses.

3. I for each mass can be described as I=mr^2. for the system, sum all 3.

4. rotational kinetic energy is similar to linear KE, 1/2Mv^2 where m is replaced by moment of inertia and v^2 is replaced by omega^2. Omega is given and I total is calculated in 3.

Answer 2

The other answer is on the right track. If you know the SUVAT (kinematic) equations for linear motion, there is an angular motion equivalent for each one. For example V = U - AT becomes Wf = Wo - alpha T in angular terms; where the two W's are angular speed in rad/sec and alpha is angular (-) deceleration in rad/sec^2. T is T for both angular and linear. Solve for T = (Wo - Wf)/alpha = ? sec, the time you're looking for. We need alpha. In SUVAT, we have V^2 = U^2 - 2aS; so the angular equivalent is Wf^2 = Wo^2 - 2 alpha Omega. Omega is the angular distance, the equivalent to S in linear terms. So alpha = Wo^2/(2 Omega) is the angular acceleration. Plug that back into the T equation. T = (Wo - Wf)//Wo^2/(2 Omega) = (Wo - Wf)(2 Omega)/Wo^2 = Wo(2 Omega)/Wo^2 = 2 Omega/Wo = 2*2*pi()*13.2/6.15 = 26.97 sec. ANS. Note that 13.2 revs is 2pi 13.2 radians = Omega. On the other hand, Wo = 6.15 rad/sec so the speed is already in radians and no conversion is needed.