A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kgm2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms–1 relative to the ground. Time taken by the man to complete one revolution is
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Step 1
Step 1: Use conservation of angular momentum to set initial angular momentum equal to final angular momentum: Initial angular momentum, L_initial = 0 Final angular momentum, L_final = MVR - Iω Show more…
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A circular platform is mounted on a vertical frictionless axle. Its radius is $r=2 m$ and its moment of inertia is $I=$ $200 \mathrm{~kg}-\mathrm{m}^{2}$. It is initially at rest. A $70 \mathrm{~kg}$ man stands on the edge of the platform and begins to walk along the edge at speed $v_{0}=10 \mathrm{~m} / \mathrm{s}$ relative to the ground. The angular velocity of the platform is (a) $1.2 \mathrm{rad} / \mathrm{s}$ (b) $0.4 \mathrm{rad} / \mathrm{s}$ (c) $2.0 \mathrm{rad} / \mathrm{s}$ (d) $0.7 \mathrm{rad} / \mathrm{s}$
A circular platform is mounted on a vertical frictionless axle. Its radius is $r=2 \mathrm{~m}$ and its moment of inertia $I=200 \mathrm{~kg} \mathrm{~m}^{2}$. It is initially at rest. A $70 \mathrm{~kg}$ man stands on the edge of the platform and begins to walk along the edge at speed $v_{0}=1 \mathrm{~m} \mathrm{~s}^{-1}$ relative to the ground. The angular velocity of the platform is (a) $1.2 \mathrm{rad} \mathrm{s}^{-1}$ (b) $0.4 \mathrm{rad} \mathrm{s}^{-1}$ (c) $0.7 \mathrm{rad} \mathrm{s}^{-1}$ (d) $2 \mathrm{rad} \mathrm{s}^{-1}$
A circular platform is mounted on a vertical friction less axle. Its radius is $r=2 \mathrm{~m}$ and its moment of inertia $I=200 \mathrm{~kg}-\mathrm{m}^{2} .$ It is initially at rest. A $70 \mathrm{~kg}$ man stands on the edge of the platform and begins to walk along the edge at speed $v_{0}=1.0 \mathrm{~ms}^{-1}$ relative to the ground. The angular velocity of the platform is $0.7 \mathrm{rad} \mathrm{s}^{-1}$. When the man has walked once around the platform, so that he is at his original position on it, his angular displacement relative to ground is (a) $\frac{6}{5} \pi$ (b) $\frac{5}{6} \pi$ (c) $\frac{4}{5} \pi$ (d) $\frac{5}{4} \pi$
Rotational Motion
Round 1
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