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Grade upto college level Mechanics

In a lecture demonstration, a toy train track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis; see Fig. A toy train of mass m is placed on the track and, with the system initially at rest, the electrical power is turned on. The train reaches a steady speed v with respect to the track. What is the angular velocity t» of the wheel, if its mass is M and its radius R? (Neglect the mass of the spokes of the wheel.)
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

Profile image of Amit Saxena
11 Years agoGrade upto college level
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Profile image of Navjyot Kalra
11 Years ago
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