Transcript Rolling

Rolling
Rotation and Translation

A rolling wheel is moving
forward with kinetic energy.

A rolling wheel is rotating
with kinetic energy.

The velocity is measured at
the center of mass.

The axis of rotation is at the
center of mass.
• Krot = ½ I w2
• KCM = ½ m v2
v
w
No Slipping

A wheel can slide, but true rolling occurs without
slipping.

As it moves through one rotation it moves forward
2pR.
w
v = 2pR/T = wR
v
R
Dx = 2pR
Point on the Edge



A point on the edge moves with a speed compared to
the center, v = wr.
Rolling motion applies the same formula to the center
of mass velocity, v = wR.
The total velocity of points varies by position.
v = 2vCM
vCM
v=0
Rolling Energy



The energy of a rolling wheel
is due to both the translation
and rotation.
The velocity is linked to the
angular velocity.
The effective energy is the
same as a wheel rotating
about a point on its edge.
• Parallel axis theorem
K  K CM  K rot
K  12 mv 2  12 Iw 2
K  12 (mR 2  I )w 2
Energy Conserved

A change in kinetic energy is
due to work done on the
wheel.
• Work is from a force
• Force acts as a torque
v
R

Rolling down an incline the
force is from gravity.
• Pivot at the point of contact

The potential energy is
converted to kinetic energy.
F = mg
q
Rolling Friction

A perfect wheel has no
sliding, so there should be
no friction.

Real wheels and ground
press together.
• Points with some velocity
• Forward component
generates friction
v>0
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