Show that the angular momentum is the product of linear momentum and `bot` distance from the axis of rotation (lever arm) i.e. L = p.d

Fill in the blanks: Torque is the product of force and __ distance from the axis of rotation.

Show that angular momentum is due to transverse component and does not depend on the radial component i.e. L = rp_theta

Show that tau = F.d . where tau is torque, F is force applied and d is the bot distance of the particle from the axis of rotation called lever arm.

Find the relation between angular momentum and lever arm.

Two particles, each of mass mand speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

Two dics of moments of inertia I_1 and I_2 about their respective axes (normal to the disc and passing through the centre), and rotating with angular speed omega_1 and omega_2 are brought into contact face to face with their axes of rotation coincident. Does the law of conservation of angular momentum apply to the situation? Why?

A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body frm the centre of the star and let its linear velocity be v, angular velocity omega , kinetic energy K, gravitational potential energy U, total energy E and angular momentum p. As the radius r of the orbit increases, determine which of the above quantities increase and which one decrease.

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show vec L = L = vec L + vecM R xx vecV where vec L = Sigma vecr_i xx vecp_i is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember vecr_i = vecr_i - vecR , rest f the notation is the standard notation used in the chapter. Note vecL and vecMR xx vecV can be said to be angular moemnta respectively about and of the centre of mass of the system of particles.