Question

There are three forces F₁, F₂ and F₃ acting on a body, all acting on a point P on the body. The body is found to move with uniform speed.

(a) Show that the forces are coplanar.

(b) Show that the torque acting on the body about any point due to these three forces is zero.

Answer 1

(a) Since the body is moving with no acceleration, the sum of the forces is zero =F₁ + F₂ + F₃ = 0. Let F₁, F₂, F₃ be the three forces passing through a point. Let F₁ and F₂ be in the plane A (one can always draw a plane having two intersecting lines such that the two lines lie on the plane). Then F₁ + F₂ must be in the plane A. Since F = - (F₁ + F₂), F₃ F is also in the plane A.

(b) Consider the torque of the forces about P. Since all the forces pass through P, the torque is zero. Now consider torque about another point 0. Then torque about 0 is

Torque = OP x (F₁ + F₂ + F₃)

Since F₁ + F₂ + F₃