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Work

Work. Let us examine the work done by a torque applied to a system. This is a small amount of the total work done by a torque to move an object a small angular distance d q. Power. Similar to. Work – Kinetic Energy. Rolling motion (No Slipping).

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Work

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  1. Work Let us examine the work done by a torque applied to a system. This is a small amount of the total work done by a torque to move an object a small angular distance dq. Power Similar to Work – Kinetic Energy

  2. Rolling motion (No Slipping) The majority of motion we have been discussing is translational motion. We have recently been exploring rotational motion. Now we will look at both together. If a wheel is placed on a flat surface and a force is applied at the center of the wheel what will it do? It will translate and rotate. Why does it rotate? It rotates due to the frictional force at the point of contact, that is in a direction opposite to the direction the wheel would slip. The rolling motion associated with this wheel can be modeled as if all parts of the wheel rotate about the point of contact. P’ Using this model, what can we say about the velocities of point P, the center and point p’? For this instant in time the point of contact would have zero velocity, the center of mass would have a velocity vCM and the top of the wheel would have a velocity twice that of the center of mass. P P v = 2vCM F v = vCM v = 0 f

  3. How can we determine the translational velocity of the center of mass when we only know the rotational speed of the wheel? We can look at the translational distance covered by the wheel. The angular velocity of the center about the contact point is the same as the angular velocity of the contact point around the center. We can also look at the acceleration of the center of mass. w Let us also look at the kinetic energy associated with rolling. S q R Translational energy S Rotational Energy

  4. Two wheels initially at rest roll the same distance without slipping down identical inclined planes starting from rest. Wheel Bhas twice the radius but the same mass as wheel A. All the mass is concentrated in their rims, so that the rotational inertias are I = mR2. Which has more translational kinetic energy when it gets to the bottom? 1. Wheel A 2. Wheel B 3. The kinetic energies are the same. 4. need more information

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