Relation Between Torque and Speed

What is Torque?

In physics, you often hear the word torque. Do you know exactly what torque means? Well, a torque is nothing but the force applied on an object to make it rotate about its axis. Therefore, any force that can cause this angular acceleration in an object is torque. 

As you can probably understand from this definition, torque is a vector quantity because both magnitude and direction of a force are at work here. The torque vector direction depends on the direction of force on the axis. 

A common question that can arise when learning about torque is its relation to speed. Therefore, listed below is the equation that pits torque vs speed.

Torque (τ) = Power/speed

This the most basic form of relation between torque and speed. If you desire to know more, you must first determine what speed is. 

Quick Exercise - 1

Q. A wheel moves at a rate of 0.3 m/s on applying a power of 40 Watts. Determine the torque acting on the wheel using a torque speed relation equation.

Solution –

Speed of the wheel is 0.3m/s

Power applied on the wheel is 40 watts

Thus, Torque = Power/speed

Torque = 40/0.3

Torque is equal to 133.33 Newton-metre 

What is Speed?

To assess torque vs speed truly, you must first understand speed in detail. Speed is nothing but the distance travelled by an object per unit of time. Speed is a scalar quantity. You do not need to establish the direction of movement to determine the speed of a body.

This is also what sets speed apart from velocity. Being a vector quantity, velocity is the speed of a body in a particular direction. 

Deriving the Relation Between Torque and Speed Formula

Since torque is a rotatory motion, we can easily derive its relation to power by comparing the linear equivalent. To determine the linear displacement, simply multiply the radius of movement with the angle covered. Keep in mind that linear displacement refers to the distance covered at the circumference of a wheel.

Therefore, we can say that Linear distance = Time x Angular velocity x Radius (eq.1) 

We know that Torque = Force x Radius

Force = Torque/Radius (eq.2)

Now, Power = Force x Linear Distance / Time

Integrating the value of force from eq.1 and eq.2, we get

Power = (Torque/Radius) x Time x Angular Velocity x Radius / Time

Thus, Power = Torque x Angular velocity

Consequently, Torque = Power/Angular velocity

What is the Relationship Between Torque and Speed?

The mathematical formula tells us that this force around an axis is inversely proportional to speed (angular velocity). This means that an increase in velocity causes torque to drop and vice versa.

Another vital factor that you need to keep in mind is that in this equation velocity and speed is used interchangeably. This is because torque, being a vector quantity, will always have speed in a particular direction. Now that you know the torque and speed relation, answer this simple question.

True or False – 1

Q. Torque is directly proportional to the radius of rotation.

Ans. True. Since torque is the product of force and radius of rotation, increasing this radius will also increase the resulting torque. The same is true for the opposite as well.

Relation Between Torque and Speed in DC Motor

In a DC motor, speed is calculated in the form of rotation per minute. Thus for such a motor, you can determine torque, by using the following formula – 

Torque = Power/ (2π x Speed of rotation)

Our online classes and a wide selection of PDF books will help you further your understanding of torque vs speed. We also have doubt-clearing sessions to ensure proper comprehension of each topic. Now, you can even download our Vedantu app to access online sessions with ease.

FAQ (Frequently Asked Questions)

1. What is the SI Unit for Measuring Torque?

Ans. The SI unit of torque is Newton-metre.

2. What is the Difference Between Torque and Force?

Ans. Torque is a force applied along an angular direction. Force, on the other hand, is any push or pull that causes a change in acceleration of the object. Therefore, torque is a vector quantity, while force is a scalar quantity.

3. If I Increase the Speed, will the Torque on the Object Increase or Decrease?

Torque is inversely proportional to speed. Thus, when speed increases, torque will decrease.