(a) The magnitude of the angular momentum about the origin of a particle of mass m moving with velocity v on a path that is a perpendicular distance d from the origin is given by m|v|d. Show that if r is the position of the particle then the vector J = r × mv represents the angular momentum. (b) Now consider a rigid collection of particles (or a solid body) rotating about an axis through the origin, the angular velocity of the collection being represented by w. (i) Show that the velocity of the ith particle is Vi = @ X ri and that the total angular momentum J is J = Σm;[r}w − (r; · w)r;]. i

(a) The magnitude of the angular momentum about the origin of a particle of mass m moving with velocity v on a path that is a perpendicular distance d from the origin is given by m|v|d. Show that if r is the position of the particle then the vector J = r × mv represents the angular momentum. (b) Now consider a rigid collection of particles (or a solid body) rotating about an axis through the origin, the angular velocity of the collection being represented by w. (i) Show that the velocity of the ith particle is Vi = @ X ri and that the total angular momentum J is J = Σm;[r}w − (r; · w)r;]. i