Question

3.A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation?

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Answer 1

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.A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation?

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Answer 2

$It \: is \: given \: that \: radius \: of \: the \: ring; \: \\ R = \frac{40}{2} = 20cm = 0.2m \: and \: mass \: of \: \\ the \: ring, m = 1 kg; V = 10 \: rotations \: s {}^{ - 1}$

$For \: ring, Moment \: of \: Inertia, \: \\ I = mR {}^{2} = 1 \times (0.2) {}^{2} = 0.04kg \: m {}^{2}$

$Angular \: velocity \: of \: the \: ring \: is \: given \\ by, ω = 2πv = 2π × 10 = 20π \: rad \: s {}^{ - 1} .$

$We \: require \: value \: of \: angular \: \\ momentum \: of \: the \: ring, which \: is \: given \: \\ by \: l = I ω = 0.04× 20π = 2.51kg \: m {}^{2} s {}^{ - 1} .$