Two disks are located on an axle as shown in the figure below. The lower disk is

Question

Two disks are located on an axle as shown in the figure below. The lower disk is initially spinning at 60 rad/s, and the upper one is not spinning. The upper disk then falls onto the lower disk, and they stick together.

(c) What is the initial angular momentum of your system?

(d) What is the final angular momentum of your system? Express your answer in terms of ?f, the final angular velocity of the two disks. (Recall that ?f has units of rad/s and angular momentum will have units of kg · m2.)

(e) Find ?f

Explanation / Answer

here,

m1 = 20 kg

R1 = 2 m

m2 = 7 kg

R2 = 1 m

C)

the initial angular momentum , Li = 0.5 * m1 R1^2 * w

Li = 0.5 *20 * 60 * 2^2

Li = 2400 kg.m^2.rad/s

D)

using conservation of enegular momentum

the initial angular momentum = final angular momentum

final angular momentum , Lf = 2400 kg.m^2.rad/s

E)

let the final angular speed be wf

Lf = ( I1 + I2) * wf

Lf = (0.5* m1 * R1^2 + 0.5 * m2 * R2^2 ) * wf

2400 = 0.5 * ( 20*2^2 + 7 * 1^2) * wf

wf = 55.17 rad/s

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