Irodov Problem 1.186

From basic projectile motion the velocity vector v and the location vector r are given by,




The angular momentum is given by,








The highest point in the trajectory occurs when the vertical component of velocity is 0 at time . At this instant the angular momentum is given by .

Irodov Problem 1.185

The moment of force or torque is the rate of change of angular momentum and so,



The angle between the torque vector and the angular momentum vector at any instant of time t is given by,








When the angle is 45 degrees we have,






The torque at this moment will be given by (1) as