Find: a) the initial angular momentum of the system. b) the final angular veloci

Question

Find:

a) the initial angular momentum of the system.

b) the final angular velocity of the system.

c) if the system reaches equilibrium in 0.20s, determine the average torque on the dropped disk.

d) what caused this torque?

Thanks!

A 0.75kg disk has a radius of 0.20m. It is initially rotating with an angular velocity of 5 rad/s about the same axis of rotation described by the figure ( a horizontal disk with axis being like a y-axis through the center like the one I tried to draw below). A second disk ( ? = 0 rad/s, mass = 0.50kg, radius = 0.30) is placed directly above the first disk and is dropped on the first disk and the system reaches equilibrium. The disks are rough (Muk = 0.20). Find: a) the initial angular momentum of the system. b) the final angular velocity of the system. c) if the system reaches equilibrium in 0.20s, determine the average torque on the dropped disk. d) what caused this torque? Thanks!

Explanation / Answer

a .
initial momentum = I1 1 = 1/2 mr^2 * 5 = 0.5 * 0.75 * 0.2^2 * 5 = 0.075

b .

conservation of angular mometum ,

I1 1 + I2 2 = ( I1 + I2 ) ;

0.075 + 0 = ( 1 /2 * 0.75 * 0.2^2 + 1 /2 * 0.5 * 0.3^2 ) ;

0.075 = 0.0375 ;

= 2 rad / s ;

c .

= change in angular moemtum / t ;

= final ang momeutm - initial ang mometum / t ;

= [ ( I1 ) - ( I1 1 ) ] / 0.2

= [ ( 0.015 ) 2 - ( 0.015 * 5 ) ] / 0.2

= 0.225 N m

d .

the friction caused the torque , there was some firction between the disks , mu k = 0.2

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