Phys 0174 Fall 2008 - Chapter 11, 4 slides

Phys 0174 Fall 2008 - Chapter 11, 4 slides - Chapter 11 t1...

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1 Chapter 11 Rolling, Torque, and Angular Momentum ¾ Rolling of circular objects and its relationship with friction ¾ Redefinition of torque as a vector ¾ Angular Momentum of single particles and systems or particles ¾ Newton’s second law for rotational motion ¾ Conservation of angular Momentum ¾ Applications of the conservation of angular momentum 2 t 1 = 0 t 2 = t Consider an object with circular cross section that rolls along a surface without slipping. We can treat this mo Rolling as Translation and R tion as a combination of: Tra otation Combin nslation of ed the center of mass Rotation of the object about the center of mass 3 t 1 = 0 t 2 = t Consider the two snapshots of a rolling bicycle wheel shown in the figure. An observer stationary with the ground will see the center of mass of the wheel move forward with a speed . The poin O t com v at which the wheel makes contact with the road also moves with the same s P peed. 4 t 1 = 0 t 2 = t During the time interval between the two snapshots both O and P cover a distance . (eqs.1) During the bicycle rider sees the wheel rotate by an angle about O so that com t s ds v dt t ds d sR R dt θ = =→= = (eqs.2) Combining equation 1 with equation 2 gives the condition for rolling without slipping: dt ω com vR =
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5 Rolling is a combination of purely translational motion with speed and a purely rotaional motion about the center of mass with angular velocity . The velocity of each point is the vector com com v v R ω = sum of the velocities of the two motions. For the translational motion the velocity vector is the same for every point ( , see figure b). com v G com vR = 6 The rotational velocity varies from point to point. The magnitude is equal to where is the distance of the point from O. The direction is tangent to the circular orbit (see figure a). The net r r velocity is the vector sum of these two terms. For example the velocity of point P is always zero. The velocity of the center of mass O is ( 0).
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This note was uploaded on 10/18/2011 for the course PHYS 101 taught by Professor Cohen during the Spring '10 term at Pittsburg State Uiversity.

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Phys 0174 Fall 2008 - Chapter 11, 4 slides - Chapter 11 t1...

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