Question

The position vector $\vec{r}$ of a particle points along the positive direction of a Z axis. If the torque of the particle is (a) Zero (b) in the negative direction of x, and (c) in the negative direction of Y, in what direction is the force causing the torque?

Answer 1

(a) The torque acting on the ball to rotate is, tau = r times F = Fr sin theta Here, theta is the angle between the force and position vector. The torque is always perpendicular to both position and force vectors. If the angle between the force and position is zero, then the torque acting on the object is zero. Therefore, the direction of the force is along z axis. (b) Since, the position is along z axis and torque is along negative x axis, the force must be perpendicular to torque and from cross product rule, the force must be along positive y axis. (c) Since, the position is along z axis and torque is along negative y axis, the force must be perpendicular to torque. From cross product rule, the force must be along positive x axis.