Chapter 2 Review of Forces and Moments - Brown University

Forces on a freely rotating wheel with negligible weight: Wheels are so ubiquitous that it’s worth
developing a short-cut to deal with them. The picture shows a generic 2D wheel, mounted onto an axle
with a frictionless bearing. The contact between wheel and ground is assumed to be ideally rough (infinite
friction).
The following trick is helpful
For a freely rotating 2D wheel, there is only one component of reaction force at the contact between the
ground and the wheel.
The picture shows a free body diagram for
a 2D wheel mounted on a frictionless
bearing.
Since only two forces act on the wheel
(the force at the axle, and the contact
force), it behaves just like a 2 force
member. The two forces must be equal
and opposite, and must act along the same
line. Moreover, the contact force must
satisfy R
Ay
> 0 .
j
A
B
i
(1)
R (2/1) By
RAy
R (2/1) By
(2)
R Ay
For a freely rotating 3D wheel, there are 2 components of reaction force acting at the contact
between the wheel and ground. One component acts perpendicular to the ground; the other acts
parallel to the ground and perpendicular to the direction of motion of the wheel (i.e. parallel to
the projection of the wheel’s axle on the ground) .
The picture below shows all the forces and moments acting on a freely rotating 3D wheel. The reactions
that act on the axle are also shown.
A view from in front of the wheel shows the directions of the forces and moments more clearly