opposite to the direction of the overall motion when it is below the level of the rolling surface (for example, any point in the part of the flange of a train wheel that is below the rail). Energy Since kinetic energy is entirely a function of an object mass and velocity, the above result may be used with the parallel axis theorem to obtain the kinetic energy associated with simple rolling Forces and acceleration Differentiating the relation between linear and angular velocity, , with respect to time gives a formula relating linear and angular acceleration . Applying Newton's second law: It follows that to accelerate the object, both a net force and a torque are required. When external force with no torque acts on the rolling object‐surface system, there will be a tangential force at the point of contact between the surface and rolling object that provides the required torque as long as the motion is pure rolling; this force is usually static friction, for example, between the road and a wheel or between a bowling lane and a bowling ball. When static friction isn't enough, the friction becomes dynamic friction and slipping happens. The tangential force is opposite in direction to the external force, and therefore partially cancels it. The resulting net force and acceleration are: has dimension of mass, and it is the mass that would have a rotational inertia at distance from an axis of rotation. Therefore, the term may be thought of as the mass with linear inertia equivalent to the rolling object rotational inertia (around its center of mass). The action of the external force upon an object in simple rotation may be conceptualized as accelerating the sum of the real mass and the virtual mass that represents the rotational inertia, which is . Since the work done by the external force is split between overcoming the translational and rotational inertia, the external force results in a smaller net force by the dimensionless multiplicative factor where represents the ratio of the aforesaid virtual mass to the object actual mass and it is equal to where is the radius of gyration corresponding to the object rotational inertia in pure rotation (not the rotational inertia in pure rolling). The square power is due to the fact rotational inertia of a point mass varies proportionally to the square of its distance to the axis. In the specific case