Example&Acirc;&nbsp;9-9

# Example&Acirc;&nbsp;9-9 - chain so the line of...

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Example 9-9 A Stationary Bike To get some exercise without going anywhere, you set your bike on a stand so that the rear wheel  is free to turn. As you pedal, the chain applies a force of 18 N to the rear sprocket wheel at a  distance of  r s  = 7.0 cm from the rotation axis of the wheel. Consider the wheel to be a hoop ( I  =  MR 2 ) of radius  R  = 35 cm and mass  M  = 2.4 kg. What is the angular velocity of the wheel after 5.0  s? PICTURE  The angular velocity is found from the angular acceleration, which is found from  Newton’s second law for rotation. Because the forces are constant, the torques is also constant.  Thus, the constant angular acceleration equations apply. Note that acts in the direction of the

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Unformatted text preview: chain, so the line of action of is tangent to the sprocket wheel, and the moment arm is the radius r s of the sprocket wheel ( Figure 9-23 ). 1. The angular velocity is related to the angular acceleration and the time: Answer: 2. Apply Newton’s second law for rotational motion to relate α to the net torque and the moment of inertia: Answer: 3. The only torque acting on the system is that due to the applied force F with moment arm r s : Answer: 4. Substitute this value for the torque and I = MR 2 for the moment of inertia: Answer: 5. Substitute into the step-1 result and solve for the angular velocity after 5.0 s: Answer:...
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Example&Acirc;&nbsp;9-9 - chain so the line of...

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