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Consider a circular disc of mass M and radius R rotating about it's centre with angular velocity w(Omega). Calculate the angular momentum of the disc about a point P situated at a distance R/2 from the center.

Consider a circular disc of mass M and radius R rotating about it's centre with angular velocity w(Omega). Calculate the angular momentum of the disc about a point P situated at a distance R/2 from the center.

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1 Answers

Suresh Sonkar
42 Points
5 years ago
Given circular disc of radius R and mass M, rotating with angular velocity ω about its centre.
Moment of inertia (I) about an axis passing through the centre (centre of mass) of the disc and perpendicular to the plane of the disc
Icm = MR2/2
Now using parallel axis theorem:
 Moment of inertia about a point P (Ip):
Ip = Icm + Md2  =  MR2/2 + M (R/2)2  = 3/4MR2
(Here d is given R/2 and Icm = MR2/2)
Angular momentum (L) about an axis passing through point P and perpendicular to the disc
 = Ipω = 3/4MR2 ω

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