In an antique shop a British shilling (disk-shaped coin) rides on an old record turntable—called a gramophone—at constant speed. The turntable has a fixed period of rotation, T=4.83 s. The coin is carefully and successively placed at ever larger radial distances from the center of the turntable (where its axis of rotation lies). The coefficient of static friction between the coin and turntable is μs=0.025. a. At an arbitrary radial distance r of the coin from the axis of rotation, what is the maximum speed Vmax the coin can have without slipping relative to the surface of the turntable? (This will be a symbolic answer in terms of μs, g, and r.) b. Use the given period of the turntable’s motion along with the answer from question a to determine the maximum distance the coin can be placed from the center of the turntable and still not slip relative to the table’s surface.
In an antique shop a British shilling (disk-shaped coin) rides on an old record turntable—called a gramophone—at constant speed. The turntable has a fixed period of rotation, T=4.83 s. The coin is carefully and successively placed at ever larger radial distances from the center of the turntable (where its axis of rotation lies). The coefficient of static friction between the coin and turntable is μs=0.025.
a. At an arbitrary radial distance r of the coin from the axis of rotation, what is the maximum speed Vmax the coin can have without slipping relative to the surface of the turntable? (This will be a symbolic answer in terms of μs, g, and r.)
b. Use the given period of the turntable’s motion along with the answer from question a to determine the maximum distance the coin can be placed from the center of the turntable and still not slip relative to the table’s surface.
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