To learn the definition and applications of angular momentum including its relationship to torque. By now, you should be familiar with the concept of momentum, defined as the product of an object's mass and its velocity: p⃗ =mv⃗ p→=mv→. You may have noticed that nearly every translational concept or equation seems to have an analogous rotational one. So, what might be the rotational analogue of momentum? Just as the rotational analogue of force F⃗ F→F_vec, called the torque τ⃗ τ→tau_vec, is defined by the formula τ⃗ =r⃗ ×F⃗ τ→=r→×F→, the rotational analogue of momentum p⃗ p→p_vec, called the angular momentum L⃗ L→L_vec, is given by the formula L⃗ =r⃗ ×p⃗ L→=r→×p→, for a single particle. For an extended body you must add up the angular momenta of all of the pieces. There is another formula for angular momentum that makes the analogy to momentum particularly clear. For a rigid body rotating about an axis of symmetry, which will be true for all parts in this problem, the measure of inertia is given not by the mass mmm but by the rotational inertia (i. e., the moment of inertia) III. Similarly, the rate of rotation is given by the body's angular speed, ωωomega. The product Iω⃗ Iω→ gives the angular momentum L⃗ L→L_vec of a rigid body rotating about an axis of symmetry. (Note that if the body is not rotating about an axis of symmetry, then the angular momentum and the angular velocity may not be parallel.)