L3_09.pptx - Rolling = Translation Rotation As you come in...

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As you come in, please set clicker to channel 44 and then answer the following question (before the lecture starts). Bug the Professor if he forgets to start the clicker software. Assuming the center of mass of the bicycle and rider are moving at +5 m/s (relative to the ground), how fast is the top edge of the wheel moving (relative to the ground)? A. +5 m/s B. 0 m/s C. -5 m/s D. +10 m/s Rolling = Translation + Rotation
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Topics for Today Rolling = Translation + Rotation (11-1) Forces and Kinetic energy of rolling (11-2) The Yo-Yo (11-3) Review of cross product (3-3) Torque as a vector (11-4) Angular momentum as a vector (11-5)
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For a wheel rolling smoothly with no slip, the point of contact has zero velocity relative to the ground. We analyze rolling as a combination of rotation and translation. The wheel axle moves with the center of mass of the bicycle, velocity = v . The wheel rotates to keep its bottom at zero velocity relative to the ground, . Rolling = Translation + Rotation
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Kinetic energy = rotation + translation Force – since the point of contact is not moving, the friction that acts is a static frictional force = f . Torque = Differentiating , we find . The translational acceleration is related to the angular acceleration of the wheel.
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