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A disk with mass m = 5.7 kg and radius R = 0.43 m hangs from a rope attached to the ceiling. The disk spins on its axis at a distance r = 1.56 m from the rope and at a frequency f = 20 rev/s (with a direction shown by the arrow).


What is the magnitude of the angular momentum of the spinning disk? ...?

Verified Answer :

The solution to the problem is as follows:

Li=Iw 
Li=1/2 MR^2 w 
w = 2piangular frequency 
Li=1/2 MR^2 (2piangular frequency) 

Substituting:

Li = 1/25.7kg0.43m^22pi*20rev/s
Li = 66.22

Therefore, the magnitude of the angular momentum is 66.22.


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Answer : \(L=66.18\ kgm^2/s\)

Explanation :


It is given that,


Mass, m = 5.7 kg


radius, R = 0.43 m


frequency, f = 20 rev/s


Angular momentum, \(L=I\omega\)


I is the moment of inertia of disk, \(I=\dfrac{MR^2}{2}\)

we know that, \(\omega = 2\pi u\)


so, \(L=MR^2\pi u\)


\(L= 5.7\ kg\times (0.43\ m)^2\times3.14\times 20\ rev/s\)

\(L=66.18\ kgm^2/s\)

Hence, the magnitude of angular momentum of spinning disk is \(66.18\ kgm^2/s\).


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