Force and Torque
We know about the definition of force in linear motion as an external agent to change the state of rest or of uniform motion in a straight line according to Newton’s first law of motion. Similarly, the rotating force is required to change the state of rest or of uniform motion in a circular motion and that rotating force is called torque.
Torque is the moment of force. In other words, The rotating effect of force can be said as a torque. for e.g: applying force to open or close the door.
Torque and expression of torque
Torque in rotational motion can be defined as the vector product of the perpendicular distance of a point of force from the axis of rotation and the force.
In Vector form:
where is the angle between and and is the unit vector along the direction of which gives the direction of .
The direction of Torque() is towards the perpendicular direction to both of and
The magnitude of is:
Some Special Cases:
1) If then . So,
2) If then . So,
So, we can define torque as the product of perpendicular force and distance from the axis of rotation.
Couple and torque due to couple
If two equal forces act on a rigid body but in opposite directions such that the body undergoes rotational motion, these forces form a couple.
Since a couple forms a rotational motion, the moment of a couple (or Torque due to a couple) can be calculated by the product of either force with the perpendicular distance between them.
The torque due to couple = Force x perpendicular distance between them.
Suppose a wheel of radius is rotating about a center ‘O’ by the application of couple as shown in figure.
Torque at point A:
Torque at point B:
The total torque on a body is:
Hence, Torque due to force = Force x perpendicular distance between two forces.
Sharing is Caring