Torque

Torque is the turning effect of force about the axis of rotation (the point at which an object rotates) which causes an object to rotate about an axis. As Force causes an object to accelerate in a linear direction, in the same way, torque causes an object to accelerate in the angular direction. It is also called the moment of force. It is denoted by the symbol ‘ τ’ (tau). Torque depends upon the magnitude of force and the moment of the arm (i.e perpendicular distance between the line of action force to the axis of rotation)

What is Torque?

The force that can cause an object to rotate along an axis is measured as torque. In linear kinematics, force is what drives an object’s acceleration. Similar to this, an angular acceleration is brought on by torque. 

As a result, torque can be thought of as the rotational counterpart to force. The axis of rotation is a straight line about which an item rotates. 

Torque in physics is only a force’s propensity to turn or twist. Torque is referred to using a variety of terms, including moment and moment of force. The moment arm or lever arm is the measurement of the separation between the point of application of force and the axis of rotation.

• The symbol used to represent is τ (tau).
• The S.I unit of Torque is N^.m (Newton-meter) or kg^.m^2.s^-2. And the CGS unit of Torque is dyne^.cm. 
• The dimension of torque is [ML²T^-2].

You may have seen the truck mechanic using a long rod for loosening the bolt of the wheel. Using long mechanics increased the magnitude of torque hence mechanics easily lose the bolt by applying less force. It is easier to open or shut the doors provided with handles near the outer edge far away from the hinges.  

Note: Torque will be directly proportional to the applied force as well as the perpendicular distance between the line of action of force to the axis of rotation (Moment of arm).  

Read More: 

• Torque on an Electric Dipole in Uniform Electric Field
• Torque on a Rectangular Current Loop

Types of Torque

The two types of torque are static and dynamic, discussed as,

1. Static Torque – Any torque that does not result in an angular acceleration is static. When someone pushes on a closed door, the door receives a static torque because, despite the exerted force, it is not spinning about its hinges. Because they are not accelerating, someone riding a bicycle at a steady speed is also creating a static torque.
2. Dynamic Torque – When a racing car accelerates off the line, the drive shaft must be creating an angular acceleration of the wheels given that the vehicle is moving quickly around the track.

How is Torque Calculated?

As shown in the above figure N denotes the axis of rotation, F is the horizontal force applied at p to rotate and d represents the moment of the arm (perpendicular distance between the line of action force to the axis of rotation).

Torque = Force × NO × sinθ

τ = F × d × sin90° [θ = 90°, NO = d]

= F × d × 1 [sin90° =1]

= F × d

Or in other words, 

τ = F × r

Therefore, Torque = Force × Moment of arm

Applications of Torque

For Torque to be applied in any system, the system must have a pivot point. These are some applications of torque:

• Riding a Bicycle,
• Pendulum,
• Seesaws and Wrenches,
• Flying Flag,
• Gyroscope, etc.

Solved Examples on Torque

Example 1: A mechanic applies a force of 400N to a wrench for loosening a bolt. He applied the force which is perpendicular to the arm of the wrench. The distance between the bolt to the hand is 60cm. Find out the torque applied.

Solution:

As mentioned in the question that the applied force is perpendicular to the arm of wrench so, the angle will be 90°.

F = 400N  

r = 60cm =  60⁄100 = .60 

Torque = F × distance × angle   

τ = F × r × sin90° 

τ = 400 × 0.60 × 1 [sin90° = 1]   

= 240 Nm 

Therefore, the magnitude of torque will be 240 Nm.

Example 2: The width of a door is 50cm. A force of 3N is applied at its edge (which is away from the hinge). Calculate the torque produced which causes the door to open. 

Solution: 

Given that,

F = 3 N  

d = 50cm = 50/100 = 0.5m    

Torque = F × d   

τ = 3 × 0.5 Nm 

= 1.5 Nm  

Hence, the torque produced will be 1.5 Nm

Example 3: A 50 N force is applied to a bar that can pivot around its center as shown in the figure below. The force is .45m away from the center at an angle of θ=45°. Find the torque on the bar.  

image

Solution: 

Given that,

Force = 50 N

Distance (r) = 45m

θ = 45°   

Torque = Frsinθ    

τ = 50 × 45 × sin 45° 

= 50 × 45 × 0.7071 [sin 45° = 0.7071] 

= 15.90975 Nm

FAQs on Torque

Question 1: What is Torque in a Car?

Answer:  

When an engine exerts itself, torque, which is a twisting force, speaks to the rotational force of the engine and quantifies how much of that twisting force is accessible.

Question 2: Is Torque a form of Energy?

Answer:

No, Torque is a form of force not the energy.

Question 3: What is the difference between Torque and Force?

Answer:

Torque is defined as the measure of the force that leads to the rotation of an objectabout its axis. While, Force is the reason that causes an object to accelerate in linear kinematics.

Question 4: What is the difference between torque and moment?

Answer:

Moment is the measurement of the angle between the rotational axis and the force’s line of action, whereas torque is the force that turns a body.

Question 5: How can we increase or decrease torque?

Answer:

Both the moment arm and the perpendicular force supplied to the moment arm can be raised to increase torque. When torque decreases, the opposite is true. When an object is at rest, its torques are balanced (they cancel out), and their sum is zero.

Question 6: Why is it difficult to open the door by pushing it or pulling it at the hinges?

Solution:

When the force is applied at hinges, the perpendicular distance between the line of action to the axis of rotation that’s r= 0, τ = rFsinθ = 0. That’s why one cannot open the door by pushing or pulling it at the hinges.

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