We often see spinning balls, spinning of wheels which causes car to move, spinning of train’s wheels, and many more rotational motions. But what is it that causes this rotational motion? It is torque.
Torques is defined as the force that is responsible for the rotational motion of the body, body rotation around the axis of rotation. We use torque in our day to day lives. When we rotate the key around the lock, that is torque. When we turn the doorknob, we apply torque. When we open the door and it swings on its hinges, that is torque. The SI unit of torque is Newton-meter (Nm).
SIMILARITY BETWEEN TORQUE AND MASS-
In linear motion we define we define force as,
F = Dp / Dt = ma
where Dp is the change in linear momentum in time Dt, m is the mass of the body and a is the acceleration of the body.
In rotational motion we define torque as the rotational analogue.
T = DL / Dt = I * a
where L is the angular momentum analogous to linear momentum p, I is moment of inertia which is analogous to mass of the body m, a is the angular acceleration which is analogous to linear acceleration a.
MATHEMATICAL FORMULA –
In linear movement, only mass and acceleration are involved to determine the force on the body. In rotational movement one more things add up. That is the distance from the fixed point or center point. Imagine when you try to push the door that is tied to a hinge. If you try to push the door near the hinge point, force to be applied is greater. If you try to push the door farther from the hinge point, comparatively less force needs to be applied.
T = F * r * sin q
Where T is the torque, F is the linear force, r is the distance between axis of rotation to the point where linear force is applied and q is the angle between F and r. While measuring q we also need to be careful about direction of linear force applied with respect to axis of rotation. In one direction its positive, in other direction its negative.
ROTATIONAL EQUILIBRIUM –
This law states that the summation of all the torques acting on a body at any instance is always zero. All the torques that apply to object, cancel each other and the net torque acting on body is Zero. In this case body does not move.