In your job as a mechanical engineer you are designing a flywheel and clutch-pla
ID: 1410864 • Letter: I
Question
In your job as a mechanical engineer you are designing a flywheel and clutch-plate system like the one in (Figure 1) . Disk A is made of a lighter material than disk B, and the moment of inertia of disk A about the shaft is one-third that of disk B. The moment of inertia of the shaft is negligible. With the clutch disconnected, A is brought up to an angular speed 0; B is initially at rest. The accelerating torque is then removed from A, and A is coupled to B. (Ignore bearing friction.) The design specifications allow for a maximum of 3500 J of thermal energy to be developed when the connection is made. What can be the maximum value of the original kinetic energy of disk A so as not to exceed the maximum allowed value of the thermal energy?
Explanation / Answer
Given that
Ib = 3*Ia
Angular momentum
L = I*w
rotational kinetic energy
K = 0.5*Iw^2
using angular momentum conservation
Li = Lf
wi*Ii = wf*If
wi = wo, Ii =Ia
If = ia + Ib = Ia + 3*Ia = 4*Ia
wf = wo*Ia/4*Ia
wf = wo/4
Kf = 0.5*If*wf^2
Kf = 0.5*4*Ia*wo^2/16
Kf = Ia*wo^2/8
Ki = Ia*wo^2/2
dK = Kf - Ki
dK = Ia*wo^2*(1/8 - 1/2) = -3*Ia*w0^2/8
given that
dK = -3500 J
3500 = 3*Ia*wo^2/8 = 3*Ki/4
maximum value of initial Kinetic energy will be
Ki = 3500*4/3 = 4666.67 J