# 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
   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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