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Vƒ A bicycle wheel of radius R and mass m is initially spinning with angular velocity wo. The wheel is lowered to the ground without bouncing. As soon as the wheel touches the level ground, the wheel starts to move forward until it begins to roll without slipping with an unknown final angular velocity w, and an unknown velocity of the center of mass v. . Assume that all the mass of the wheel is located on the rim, thus take the moment of inertia to be I = mR². The coefficient of kinetic friction is μk between wheel and ground. (a) What is the velocity of the center of mass of the wheel Vƒ when it begins to roll without slipping in terms of wo and R? Draw a free-body diagram and indicate all forces acting. (b) How far has it traveled when it begins pure rolling in terms of R, g, μk and wo? (c) If the wheel with the speed calculated in (a) were to go up a very long frictionless incline plane, what is the highest vertical distance it can reach? Calculate the height in terms of R, g and wo

Vƒ A bicycle wheel of radius R and mass m is initially spinning with angular velocity wo. The wheel is lowered to the ground without bouncing. As soon as the wheel touches the level ground, the wheel starts to move forward until it begins to roll without slipping with an unknown final angular velocity w, and an unknown velocity of the center of mass v. . Assume that all the mass of the wheel is located on the rim, thus take the moment of inertia to be I = mR². The coefficient of kinetic friction is μk between wheel and ground. (a) What is the velocity of the center of mass of the wheel Vƒ when it begins to roll without slipping in terms of wo and R? Draw a free-body diagram and indicate all forces acting. (b) How far has it traveled when it begins pure rolling in terms of R, g, μk and wo? (c) If the wheel with the speed calculated in (a) were to go up a very long frictionless incline plane, what is the highest vertical distance it can reach? Calculate the height in terms of R, g and wo

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Vƒ A bicycle wheel of radius R and mass m is initially spinning with angular velocity wo. The wheel is lowered to the ground without bouncing. As soon as the wheel touches the level ground, the wheel starts to move forward until it begins to roll without slipping with an unknown final angular velocity w, and an unknown velocity of the center of mass v. . Assume that all the mass of the wheel is located on the rim, thus take the moment of inertia to be I = mR². The coefficient of kinetic friction is μk between wheel and ground. (a) What is the velocity of the center of mass of the wheel Vƒ when it begins to roll without slipping in terms of wo and R? Draw a free-body diagram and indicate all forces acting. (b) How far has it traveled when it begins pure rolling in terms of R, g, μk and wo? (c) If the wheel with the speed calculated in (a) were to go up a very long frictionless incline plane, what is the highest vertical distance it can reach? Calculate the height in terms of R, g and wo
Transcribed Image Text:Vƒ A bicycle wheel of radius R and mass m is initially spinning with angular velocity wo. The wheel is lowered to the ground without bouncing. As soon as the wheel touches the level ground, the wheel starts to move forward until it begins to roll without slipping with an unknown final angular velocity w, and an unknown velocity of the center of mass v. . Assume that all the mass of the wheel is located on the rim, thus take the moment of inertia to be I = mR². The coefficient of kinetic friction is μk between wheel and ground. (a) What is the velocity of the center of mass of the wheel Vƒ when it begins to roll without slipping in terms of wo and R? Draw a free-body diagram and indicate all forces acting. (b) How far has it traveled when it begins pure rolling in terms of R, g, μk and wo? (c) If the wheel with the speed calculated in (a) were to go up a very long frictionless incline plane, what is the highest vertical distance it can reach? Calculate the height in terms of R, g and wo
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