Rotation 2 Question 11

11. A disc of mass M and radius R is rolling with angular speed ω on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is

(1999, 2M)

(a) 12MR2ω

(b) MR2ω

(c) 32MR2ω

(d) 2MR2ω

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Answer:

Correct Answer: 11. (c)

Solution:

  1. From the theorem

(a)

(b)

L0=LCM+M(r×v)

We may write

Angular momentum about O= Angular momentum about CM+ Angular momentum of CM about origin

L0=Iω+MRv=12MR2ω+MR(Rω)=32MR2ω

NOTE That in this case [ Figure (a) ] both the terms in Eq. (i), i.e. LCM and M(r×v) have the same direction A¨. That is why, we have used L0=/ω+MRv. We will use L0=∣ωMRv if they are in opposite direction as shown in figure (b).



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