Here we will consider a simple conservation-of-angular- momentum problem in whic
ID: 1409291 • Letter: H
Question
Here we will consider a simple conservation-of-angular- momentum problem in which two disks apply torques to each other, thereby causing each disk's angular momentum to change. But the total angular momentum of the two-disk system remains unchanged because there are no external torques. (Figure 1) shows the two disks, one an engine flywheel and the other a clutch plate attached to a transmission shaft. Their moments of inertia are I_A and I_B; initially, they are rotating with constant angular velocities omega_A and omega_B; respectively. We then push the disks together with forces acting along the axis, so as not to apply any external torque to either disk. The disks rub against each other and eventually reach a common final angular velocity omega_f. Derive an expression for omega_f. SOLUTION SET UP The two disks are an isolated system. The only torque acting on either disk is the torque applied by the other disk; there are no external torques. Thus the total angular momentum of the system is the same before and after they are pushed together. At the end, they rotate together as one body with total moment of inertia I_f = I_A + I_B and angular velocity omega_f. SOLVE Conservation of angular momentum gives I_Aomega_A + I_Bomega_B = (I_A + I_B)omegs_f omega_f = I_A omega_A + I_B omega_B/I_A+I_B REFLECT This is the analog of a completely inelastic collision of two particles. The final kinetic energy is always less than the initial value. This can be proved in general by using the above expression for omega_f. Suppose I_B = 2I_A. How must omega_A and omega_B be related if the entire system comes to rest after the interaction?Explanation / Answer
partA:
in this main condition is Ia Wa+IbWb=(Ia+Ib)Wf
the angular velocity Wf=0
IaWa+IbWb=0.............................(1)
but Ib=2Ia
the Ib value is substitute in eq 1 we get relation of Wa and Wb
IaWa+2IaWb=0
IaWa=-2IaWb
Wa=-2Wb..............................(2)
the correct option is B