Rolling Motion

1
Chapter 11

• Rolling Motion

2
Rolling motion

• Rolling with slippingsurfaces can move with
  respect to the point of contact
• Frictionless or low friction
• No simple relationship between rotational and
  translational motion

3
Rolling motion

• Rolling without slippingsurface 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

4
Angular Momentum

• Definition of angular momentum (L)
• Direction defined by right hand rule
• Same direction as angular velocity
• Newtons 2nd Law
• Torque is the rate of change of angular momentum

5
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 (Newtons 3rd Law)

6
Angular Momentum

• Angular momentum is conserved
• If moment of inertia (I) is changed, angular
  velocity (?) must change
• Figure skaters

Conservation problem, p. 279
7
Equilibrium

• Translational equilibrium
• ?F 0
• No net force
• Rotational equilibrium
• ?? 0
• No net torque
• Static Equilibriumno movement
• Kinetic Equilibriumconstant velocity

See-saw Meter stick, page 258
8
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

9
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