if a force F acts on an object such that its lever arm is zero, does it have any effect on the object's motion

Question

if a force F acts on an object such that its lever arm is zero, does it have any effect on the object's motion? explain

Answer 1

No torque (twisting) is imposed if the force F acts through the center of mass (CM). We can think of CM as the axis of rotation, like a fulcrum on a teeter totter. So if the force is applied some distance d from the fulcrum at the CM, we would have Fd = torque and the mass would twist. But as d = 0 in your case, torque is zero and there is no twisting.

On the other hand, as the force is applied to the CM (d = 0), we have F = ma and a = F/m; so that the mass m (mathematically located at CM) would accelerate.

Answer 2

I'm assuming lever arm as you use it is the cross product of force and distance. If your force, or your distance, or both, are zero, you'll have zero torque, and your object's orientation will not change.

If your force acts directly on the center of mass of the object, your torque may be zero, but you will still cause a linear acceleration, thus changing the motion.