Torque is the effect of force when it is applied to an object containing a pivot point or the axis of rotation (the point at which an object rotates), which results in the form of rotational motion of the object. The Force causes objects to accelerate in the linear direction in which the force is applied, but in the case of torque, it causes objects to accelerate in the angular direction with respect to the axis of rotation. Torque is also called the “moment of force,” as it depends on the magnitude of the force as well as the moment of the arm, i.e., the perpendicular distance between the line of action force and the axis of rotation. Torque is as fundamental to rotational motion as force is to a straight-line motion. In this article, we will learn about torque and how torque has a tendency to cause rotation, also how to solve numerical problems based on Torque as well.
Torque Definition
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.
What is Torque?
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.
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.
Torque Formula is given by the cross product between Force and the displacement vector from the pivot point. Thus, mathematically torque can be written as:
Torque = Force × Displacement Vector
OR
[Tex]\bold{\tau = \vec{r}\times\vec{F} = rF\sin\theta }[/Tex]
Where θ is the angle between vector r and vector F.
Unit and Dimension of Torque
The SI unit of Torque is N-m (Newton-meter) or kg.m2.s-2. Other than this, some other units of Torque include dyne-cm, pound-feet, and pound-inches.
The dimension of the Torque is force multiplied by the distance, i.e., [MLT-2] × [L] = [ML2T-2], where [M] represents a dimension of mass, [L] represents a dimension of length, and [T] represents a dimension of time.
How is Torque Calculated?
As shown in the 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 × Perpendicular
τ = F d × sin90° [θ = 90°, NO = d]
τ = F × d × 1 [sin90° =1]
τ = F × d
Or in other words,
τ = F × r
Therefore, Torque = Force × Moment of arm
Measurement of Torque
The unit of torque torque is measured in Newton-meters (N-m). This equation can be expressed as the result of multiplying force and position vectors.
Also Check:
Types of Torque
The two types of torque are static and dynamic, discussed as follows:
- Static Torque
- Dynamic Torque
Let’s learn about various types of torque in detail below.
Static Torque
Any torque that does not result in an angular acceleration is called static torque. 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. Some other examples of static torque include tightening of the bolt with the help of a wrench, opening the caps of bottles using a bottle opener, turning the steering wheel of the vehicle, etc.
Dynamic Torque
The torque that results in angular acceleration is called 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. Also, when you are riding a bicycle, you start pedalling and the bicycle starts to move at varying speeds, which is also an example of dynamic torque. Some more examples of dynamic torque include Spinning a top, operations of a wind turbine, and use of a power drill.
Applications of Torque
For Torque to be applied in any system, the system must have a pivot point. These are some applications of torque:
Automotive Industry
In automobile industries, torque is equivalent to the measurement of the power of the engine. It is used to market a vehicle’s power side by side with the horsepower of the engine. In automobiles, the engine produces torque which is further transmitted by transmission to the wheel and makes the vehicle go forward and backward.
Construction
In construction, many equipment and technique are the results of the application of torque. The most common application of torque in construction can be seen in the tightening of the screw and bolts. There is a equipment called torque wrench which can apply a very specific amount of torque to a bolt or screw, ensuring precise tightening.
Sports
Torque is used by many players in various games such as golf, baseball, and tennis. For example, in gold, the player uses the torque generated by the rotation of the body of the golfer to generate more power for the shot and transmit that power to the ball using the gold club.
Robotics
In Robotics, torque is used for the movement of the arms and other joints of the body of the robot. The motor placed in the various parts of the robot generates torque. which allow the robot to move very precisely and perform various task.
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How is torque calculated?
Torque is calculated by multiplying the force applied with the distance from the point of rotation (lever arm). The formula is represented as
Torque = Force × Distance
What factors affect torque in a vehicle?
In vehicles, torque is influenced by several factors including the engine size, the air intake quantity, the fuel type, and the efficiency of the engine’s internal mechanisms. Turbocharged engines often provide more torque at lower RPM compared to naturally aspirated engines due to the increased air intake pressured by the turbo system.
Why is torque important in cars?
Torque is crucial in vehicles as it directly impacts the vehicle’s ability to accelerate. Higher torque means better initial acceleration from a standstill, which is essential for performance in passenger cars and critical for towing and hauling in trucks.
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 × sin θ
⇒ τ = F × r × sin 90°
⇒ τ = 400 × 0.60 × 1 [sin 90° = 1]
⇒ τ = 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
r = 50cm = 50/100 = 0.5m
As, most efficient way to open the door, if the force applied to the edge of door is perpendicular to the plane of door, θ = 90°
Torque = F × r × sin θ
⇒ τ = 3 × 0.5 × 1 [sin 90° = 1]
⇒ τ = 1.5 Nm
Hence, the torque produced will be 1.5 Nm
Example 3: A motor exerts a torque of 100 N·m on a shaft that has a radius of 0.5 meters. What force is exerted by the motor on the shaft?
Solution:
The force exerted by the motor can be calculated using the formula.
τ = F x r
where τ is the torque, F is the force applied, and r is the radius of the shaft.
Given: τ = 100 N·m, r = 0.5 meters.
F = τ / r
⇒ F = 100 / 0.5
⇒ F = 200 N
So the force exerted by the motor on the shaft is 200 N.
Example 4: A 50 N force is applied to a bar that can pivot around its centre as shown in the figure below. The force is .45m away from the centre at an angle of θ = 45°. Find the torque on the bar.
image
Solution:
Given that, Force = 50 N,
Distance (r) = 45m
and θ = 45°
Torque = F × r × sin θ
⇒ τ = 50 × 45 × sin 45°
⇒ τ = 50 × 45 × 0.7071 [sin 45° = 0.7071]
⇒ τ = 15.90975 ≈ 15.91 Nm
The torque applied on the bar is 15.91 Nm
Torque – FAQs
What is Torque?
The twisting and turning force that is responsible for the motion of an object is called Torque. Torque is calculated by multiplying the force applied to the arm length. It is calculated in Joule.
What is Torque in a Car?
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.
Is Torque a form of Energy?
No, Torque is a form of force not the energy.
What is the difference between Torque and Force?
Torque is defined as the measure of the force that leads to the rotation of an object about its axis. While, Force is the reason that causes an object to accelerate in linear kinematics.
What is the Difference Between Torque and Moment?
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.
How can we Increase or Decrease Torque?
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.
Why is it Difficult to Open the door by Pushing it or Pulling it at the Hinges?
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 = rFsin(θ)
τ = 0
That’s why one cannot open the door by pushing or pulling it at the hinges.
When Torque is Zero?
If the rotating force is applied at the point of rotation of the arm then the torque produced is zero.
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