a uniform horizontal circular disc of mass m and radius r can freely rotate
Answers
The angular velocity of the disc is ω f = 4/5 ω i
Explanation:
Correct statement:
A uniform horizontal circular disc of mass MM and radius RR can freely rotate about a vertical axle passing through its centre. A particle of mass mm is placed near the centre of the disc in a smooth groove made along the radius of the disc as shown. An initial angular velocity ω^ 2 is imparted to the disc. Find the angular velocity of the disc, when the particle reaches the other end of the groove. (Take M/m =4)
Solution:
No extend force so total angular momentum is constant
I1ωf = I,ω i
ω f = (li / lf)ω ;
li = 1/2 MR^2 + 1/2 M(0)^2 = 1/2 MR^2 (M = 4x)
l = 2MR^2
lf = 1/2 MR^2 + 1/2M(R)^2 = 5/2 MR^2
li / lf = 4/5
ω f = 4/5 ω i
Thus the angular velocity of the disc is ω f = 4/5 ω i
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