Rolling_Racers_-_Moment_of_inertia.ogv (Ogg Theora video file, length 6.2 s, 625 × 352 pixels, 566 kbps, file size: 431 KB) The objects are, from back to front: At any moment in time, the forces acting on each object will be its weight, the normal force exerted by the plane on the object and the static friction force.
However, the force due to friction acts perpendicular to the contact point, and therefore it does result in a torque, which causes the object to rotate.
Since there is no slipping, the object's center of mass will travel with speed
, where r is its radius, or the distance from a contact point to the axis of rotation, and ω its angular speed.
Since static friction does no work, and dissipative forces are being ignored, we have conservation of energy.
, we obtain: Since the torque is constant we conclude, by Newton's 2nd Law for rotation
: This final result reveals that, for objects of the same radius, the mass the object are irrelevant and what determines the rate of acceleration is the geometric distribution of their mass, which is represented by the value of k. Additionally, we observe that objects with larger values of k will accelerate more slowly.