<P> is the matter's momentum . Referring this momentum to a central point introduces a complication: the momentum is not applied to the point directly . For instance, a particle of matter at the outer edge of a wheel is, in effect, at the end of a lever of the same length as the wheel's radius, its momentum turning the lever about the center point . This imaginary lever is known as the moment arm . It has the effect of multiplying the momentum's effort in proportion to its length, an effect known as a moment . Hence, the particle's momentum referred to a particular point, </P> <Dl> <Dd> (moment arm) × (amount of inertia) × (amount of displacement) = moment of (inertia displacement) length × mass × velocity = moment of momentum r × m × v = L (\ displaystyle (\ begin (aligned) ((\ text (moment arm))) \ times ((\ text (amount of inertia))) \ times ((\ text (amount of displacement))) & = (\ text (moment of (inertia displacement))) \ \ (\ text (length)) \ times (\ text (mass)) \ times (\ text (velocity)) & = (\ text (moment of momentum)) \ \ r \ times m \ times v& = L \ \ \ end (aligned))) </Dd> </Dl> <Dd> (moment arm) × (amount of inertia) × (amount of displacement) = moment of (inertia displacement) length × mass × velocity = moment of momentum r × m × v = L (\ displaystyle (\ begin (aligned) ((\ text (moment arm))) \ times ((\ text (amount of inertia))) \ times ((\ text (amount of displacement))) & = (\ text (moment of (inertia displacement))) \ \ (\ text (length)) \ times (\ text (mass)) \ times (\ text (velocity)) & = (\ text (moment of momentum)) \ \ r \ times m \ times v& = L \ \ \ end (aligned))) </Dd> <P> is the angular momentum, sometimes called, as here, the moment of momentum of the particle versus that particular center point . The equation L = r m v (\ displaystyle L = rmv) combines a moment (a mass m (\ displaystyle m) turning moment arm r (\ displaystyle r)) with a linear (straight - line equivalent) speed v (\ displaystyle v). Linear speed referred to the central point is simply the product of the distance r (\ displaystyle r) and the angular speed ω (\ displaystyle \ omega) versus the point: v = r ω, (\ displaystyle v = r \ omega,) another moment . Hence, angular momentum contains a double moment: L = r m r ω . (\ displaystyle L = rmr \ omega .) Simplifying slightly, L = r 2 m ω, (\ displaystyle L = r ^ (2) m \ omega,) the quantity r 2 m (\ displaystyle r ^ (2) m) is the particle's moment of inertia, sometimes called the second moment of mass . It is a measure of rotational inertia . </P>

Difference between angular momentum and moment of inertia