Chapter 11 Rolling Motion by os8lO1GE

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									Chapter 11
Rolling Motion
Rolling motion
  Rolling with slipping—surfaces can
  move with respect to the point of
  contact
     Frictionless or low friction
     No simple relationship between rotational
      and translational motion
  Rolling motion
    Rolling without slipping—surface do not
    move with respect to the point of
    contact
       Direct relationship between rotational and
        translational motion
       s = distance traveled by the center of mass
       vcm = velocity of the center of mass
       acm = acceleration of the center of mass

s  r           vcm  r            acm  r
Angular Momentum
 Definition of angular momentum (L)
             L  I
     Direction defined by right hand rule
        Same direction as angular velocity
 Newton’s 2nd Law
     Torque is the rate of change of angular
      momentum                L
                          
                                 t
Angular momentum
 Angular momentum remains unchanged
 in the absence of a net torque
 Spinning objects are more stable for
 this reason
     Bicycles, gyroscopes, footballs, frisbees,
      boomerangs
     Helicopters (Newton’s 3rd Law)
     Angular Momentum
          Angular momentum is conserved
          If moment of inertia (I) is changed,
          angular velocity () must change
             Figure skaters




Conservation problem, p. 279
     Equilibrium
           Translational equilibrium
               F = 0
               No net force
           Rotational equilibrium
                = 0
               No net torque
           Static Equilibrium—no movement
           Kinetic Equilibrium—constant velocity
See-saw
Meter stick, page 258
Stability
  Stable equilibrium
      Displacements from equilibrium result in a
       restoring force or torque
      Tends to return to equilibrium when disturbed
      Ball in a bowl
  Unstable equilibrium
      Displacements from equilibrium result in a force or
       torque that moves it further away
      Tends to move away from equilibrium
      Ball on top of a bowl
      Stability
           Conditional equilibrium
               Stable as long as the center of mass is
                directly above the base of support
               Unstable if the center of mass is not
                located directly over the base of support
           Examples
               Refrigerator
               Ships

Stacking bricks, p 264

								
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