#turningeffectofforces #torque #textbook #physics

Ch:- 4

Pg:- 67,68

The turning effect of a force, also known as torque or moment of force, refers to the tendency of a force to rotate an object around a pivot point or axis. The turning effect depends on both the magnitude of the applied force and its distance from the pivot point.

1. Torque Definition

Torque (T) is a measure of how effectively a force can cause an object to rotate. Mathematically, torque is defined as the product of the force applied and the perpendicular distance from the pivot point (or axis of rotation) to the line of action of the force. The formula for torque is:

T=F⋅d

Where:

• T is the torque (in Newton-meters, Nm),

• F is the magnitude of the force (in Newtons, N),

• d is the perpendicular distance from the pivot point to the line of action of the force (in meters, m).

2. Line of Action and Perpendicular Distance

The line of action of a force refers to the straight line along which the force is applied. The perpendicular distance is the shortest distance from the pivot point to this line of action. The larger the perpendicular distance (also called the lever arm), the greater the torque generated by the same force.

3. Direction of Torque

The direction of torque is determined by the direction in which the force tends to rotate the object. Using the right-hand rule, if you curl the fingers of your right hand in the direction of rotation that the force causes, your thumb will point in the direction of the torque vector.

• Clockwise rotation typically corresponds to negative torque.

• Counterclockwise rotation typically corresponds to positive torque.

4. Balancing Torques (Equilibrium)

If multiple forces are acting on an object, their torques can either oppose or reinforce each other. For an object to be in rotational equilibrium, the sum of all torques acting on it must be zero

5. Real-world examples of the Turning Effect of Forces

• Opening a door: When you push on a door at a distance from the hinge (the pivot point), you exert a torque that causes it to rotate. The farther from the hinge you push, the easier it is to open the door.

• Using a wrench: When tightening or loosening a bolt with a wrench, you apply a force at the end of the wrench. The length of the wrench provides a long lever arm, increasing the torque and making it easier to turn the bolt.

• Balancing a seesaw: To balance a seesaw, the torques exerted by the weights of individuals on both sides need to be equal. If one person sits farther from the pivot than the other, their smaller weight can generate the same torque as a larger weight that is closer to the pivot.

6. Factors Affecting Torque

• Magnitude of the Force: A greater force increases the torque.

• Distance from the Pivot: A longer lever arm (distance) increases the torque.

• Angle of Force Application: Torque is maximized when the force is applied perpendicularly to the lever arm. If the force is applied at an angle, only the component of the force that is perpendicular to the lever arm contributes to the torque. This is given by the modified equation:

  
  

  T=F⋅d⋅sin⁡(θ)

  
  

  Where θ is the angle between the force and the lever arm.