Torque, definition, applications, direction, practice problems, FAQs

Everyone has played on see-saw once in their lifetime. Ever wondered why it tries to settle towards the person having more weight or why it becomes horizontal in some cases such as both the persons sitting are of same mass. To know the reason, you need to have the knowledge about the concept of torque.

Table of contents

• Torque
• Direction of torque
• Torque about an axis
• Applications of torque
• Practice problems
• FAQs

Torque

The capability of a force to change the state of  rotational motion of a body is known as torque.

• It is the measure of a force that causes an object to rotate about an axis and change its angular velocity.
• Torque can also be understood as the angular counterpart of force.

possibility of the rotation happening or not depends on the magnitude of the force applied and the position of the application of force. For example, if we try to open a door, the magnitude of the force that is needed to open the door varies with the distance from the hinge. If the point of application of the force is moved away from the hinge, then the force required will be reduced. If the point of application of the force is moved closer to the hinge, then the magnitude of the force required will be more for the same amount of rotation.

Let us consider an object that rotates about an axis passing through O.

The applied force is at a point P and the position vector is r as shown in the figure.

Then, the torque produced by force F on the system about Z axis is given by,

Torque is a cross product of the force applied and the position vector of the point at which the force is applied. SI unit or torque is Nm. dimension of torque is  [M¹L²T^-2].

We can expand the given equation as,

n  is the direction of torque according to the right hand rule of cross product.

Torque is an axial vector and its direction is determined using the right-hand thumb rule.

The direction of torque is perpendicular to the plane containing 

Direction of torque

Right-Hand Thumb Rule

Place your fingers along the position vector r, curl the fingers of your right hand in the direction of the force vector F, and your thumb will give the direction of torque.

Force Arm

Let us consider a body which is rotated by applying force  at point P with position vector . The position vector is making an angle θ with the force vector as shown in the figure.

Then, the torque is calculated as,

The perpendicular distance of the line of action of the force from point O is known as the force arm.

The force arm is equal to .

Only the component perpendicular to the position vector contributes to the torque that causes the rotation of the object.

Torque can also be calculated by taking the component of force perpendicular to the position vector.

Torque About an Axis

We know that torque of the force  on the system shown in the figure about point O is given by the following equation:

Here, torque of the force  about line AB will be the component of  _o along the same line.

Points to Remember

Applications of torque

1. Concept of torque is used in the dams where water falling on the turbines provides torque to rotate the shaft of the dynamo which is used for generating electricity.
2. The process of churning of milk is carried out by applying the torque using the ropes that in turn rotates the handle.
3.The reason we are so easily able to open doors is one of the most common applications of the concept of torque.

Practice problems

Q1. If  is the force acting on a particle having position vector  and  is the torque of this force about the origin, then which of the following is true?

A: (a)

Solution. As the particle is in the xy-plane, the force is also shown to be in the xy-plane. Both  and  are perpendicular to the torque vector that lies in the z-direction.

Q2. A particle of mass M is released in a vertical plane from point P at x = x0 on the x-axis. It falls vertically along the y-axis. Find the torque (𝜏) acting on the particle at time t about the origin.

A.  The weight is the force that is acting on the particle in the downward direction.

Solution. The magnitude of torque in this case can be given as follows:

Direction is found using the right-hand thumb rule. It will be directed along the z-axis or in the clockwise direction, or pointed towards the inside of the screen.

Thus,

Q3. Find the torque of force  on the particle about points O and A.

A. The torque about point O is as follows:

Q4. Find the torque of weight about the axis passing through point P.

A.

We know that the torque of the weight about point P can be written as follows:

𝜏 = (r)(F⊥) = R(mg sin 𝜃) = mgR sin 𝜃

Direction can be found using the right-hand thumb rule. Here, it is in the clockwise direction. The torque is the same about the axis passing through point P.

FAQs

Question 1. What is the difference between torque and moment?
Answer. Concept of torque is used when there is rotation involved and moment is used when rotation is absent or rather you can say it has tendency to rotate the object.

Question 2. What is the dimensional formula for torque?
Answer. [ML²T^-2]

Question 3. How is a long arm wrench able to open a bolt or a nut more easily as compared to a wrench with a smaller arm?
Answer. To open a bolt or nut, one needs to apply larger torque. One method is to increase the force which is limited by a person's capability. Another method is to increase the arm length which is being used in the longer wrenches to increase the torque.

Question 4. Is torque a scalar or vector quantity?
Answer. Torque is a vector quantity since it has both magnitude and direction.