What is torque exactly and why is torque perpendicular to force and radius? ?

Question

From what I understand about torque, it is basically the power of the force to cause a change in an object's rotational motion. It is easier to cause this change when the force is applied further from the point of rotation than closer, which is why it is difficult to open a door by pressing a millimeter from the hinges, but much easier by pushing on the door a meter from the hinges.

However, I do not understand why the torque is the cross product of the force and radius. If I use a wrench and push on it, why is torque perpendicular to the force? I thought it would be in the same direction as the force. But it is perpendicular which seems to be counterintuitive as neither the force, the radius, or the change in angular motion is involved in that direction. What is torque meant to calculate then, and how does it make sense?

Answer 1

You need a force to set a body in linear motion. Likewise you need a torque to rotate a body Thus torque plays a similar role as does force. Like force torque is also a vector quantity but in linear motion force is in the direction of motion . In case of rotational motion torque vector is perpendicular to the place carrying force and force arm.

Force = Mass* acceleration

Torque = Force* Force arm

Force = M*a

Torque = Moment of Inertia* Angular Acceleration ( MOI plays similar role as mass in linear motion)

Likewise we have other formulae for rotational motion