NEET Class neet Answered
.A heavy disc is thrown on a horizontal surface
in such a way that it slides with a speed V
initially without rolling. It will start rolling
without slipping when its speed is reduced
Asked by mvenkataram | 30 Aug, 2019, 10:35: AM
Expert Answer
When the disc is slipping without rolling, there is no external torque is acting on the disc.
Hence angular momentum is conserved.
Let u be initial speed of disc, m is its mass and R be its radius.
Initial angular momentum = m u R .........................(1)
when it start rolling, let ω be its angular speed .
If I is moment of inertia of the disc about its contact point, then final angular momentum = Iω .
Hence, ( m u R ) = Iω ...........................(2)
Moment of inertia of disc about its contact point = (1/2)MR2 + MR2 = (3/2)MR2 .........................(3)
linear speed of disc v when it is rolling is given by, v = ω R .........................(4)
By substituting for I and ω in eqn.(2), we get, ( m u R ) = (3/2)MR2 (v/R) or v = (2/3) u
Hence when the disc speed is reduced to (2/3) of its initial speed, disc will start rolling
Answered by Thiyagarajan K | 30 Aug, 2019, 11:36: AM
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