Dikshant SavantApr 15, 2026

Understanding Torque: Line of Action Explained 📐

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Understanding Torque: Line of Action Explained 📐

Dikshant Savant

Understand the physics behind torque by exploring why we use the line of action versus the point of application. This video breaks down the math behind the cross product to help you visualize torque in real-world scenarios like opening a door.

Understanding Torque: Line of Action Explained 📐

Dikshant Savant

Understand the physics behind torque by exploring why we use the line of action versus the point of application. This video breaks down the math behind the cross product to help you visualize torque in real-world scenarios like opening a door.

Chapters

00:00

Introduction

Introduction to the user's question about the definition of torque.

00:38

Understanding Torque Definition

01:00

The Door Analogy

02:14

Calculating Torque Components

04:18

Practical Torque Example

06:45

Finding Torque Direction

07:26

Conclusion

Transcript

00:00

Hello.

00:00

I saw your question on Reddit, and, it's a fascinating question.

00:05

Really like it.

00:06

So let's dig deep into it.

00:08

Okay, so here you're asking basically about torque and how and why it operates the way it does.

00:16

Sorry about that.

00:18

My pen is just flickering.

00:20

Okay, so you said that I'm studying torque right now, and definition keeps saying torque is force times perpendicular distance from the pivot to the line of action of force.

00:28

You understand that the part when the force is at an angle.

00:30

But why do you use the line of action instead of just measuring to the point where the force is applied?

00:35

Right, so let's take a very simple example.

00:37

so first let's talk about the definition.

00:40

Torque vector is R cross F.

00:42

Okay?

00:43

R cross F.

00:46

basically that is RF sine of the angle between them, right?

00:51

So it can be written like this, or it can be written as F times R sine theta.

00:58

Right?

00:58

Why am I saying all this?

01:00

Let's take a look at this.

01:01

Okay, so let's assume you have a door, and this is the hinge of the door, and this is your door, okay?

01:09

So it can rotate like this and this direction.

01:12

So let's assume, like, you apply a force in this direction, okay?

01:17

A force in this direction, to pull the door.

01:21

So this won't rotate it, right?

01:24

Because it is directly in line with, the axis.

01:29

And if I apply in like, let's say, any other direction or a perpendicular direction from this door, it will turn the door.

01:36

Right?

01:38

So basically why I'm telling you this is, say a force is applied at any point and the distance is R.

01:52

Okay?

01:53

And the distance, the angle between R and F is theta.

01:58

So the torque applied around this point, around, this hinge, O can be written in two ways, okay?

02:08

So look at this.

02:09

Either I can take the component of force, or I can take the component of R.

02:14

First, let's take the component of force.

02:16

So there are two components of force for this.

02:20

One is in perpendicular direction and one is in direction of R.

02:25

So this is F cos theta, and this is F sin theta.

02:30

Now, this F cos theta is the similar force like this that is operating through the hinge of this, table, right?

02:40

So this won't produce any torque.

02:42

What will produce torque is this sign component of force.

02:46

So in my first case, I broke down force, okay?

02:49

So the torque will be equal to R times F sin theta.

02:53

And if you look at it, it's basically the component of force that is perpendicular to the distance between them or the radial distance between them.

03:04

Otherwise, let's take a look at this in another way.

03:08

Instead of breaking force, I can also break down R.

03:12

So if this is R, this is theta, the angle between force and R, then I.

03:19

Then that means this is theta.

03:21

And if this is theta, I can have two components of theta, right?

03:26

One along the direction of force like this, and one perpendicular to the direction of force like this.

03:34

Right?

03:35

And this is R cos theta, and this is R sine theta.

03:39

So R sine theta is basically the distance, perpendicular distance to the line of force.

03:48

Right?

03:49

So that means my torque is.

03:52

So this, So this distance is what is essentially causing the torque.

04:00

Because if this distance becomes zero, torque becomes zero.

04:03

Right?

04:04

So in this case we can write force times R.

04:07

Sine theta is the torque which is the same in both the cases, which is the same as this as we wrote.

04:14

Right?

04:14

So mathematically it's all the same.

04:18

So here you can understand, like, not just to mug it up, that either you can take, let's say.

04:28

So either you can take like, Let's say there is a door.

04:32

And this is the hinge.

04:35

Either.

04:36

So, Okay, let's take a look from the top.

04:40

Okay.

04:41

This is the door, and this is the hinge.

04:43

Okay?

04:44

So let's say I apply a force like F like this over here.

04:47

And let's say this angle is 60 degrees.

04:49

Okay?

04:50

let's say this, door has a length L, right?

04:55

So I can do this two ways.

04:56

Either I can break F or I can break L.

05:00

L is the radial distance between the hinge and the, force.

05:04

This is the top view.

05:06

Okay?

05:06

So just so you don't get confused, this is the top view of the door.

05:10

And if I can draw the handle.

05:13

Yeah, this is the handle.

05:14

Okay, now, we'll do it both ways so you understand it completely.

05:20

So if this is my L, this is my F, and the angle is 60 degrees.

05:26

That means first, either I can divide force or I can divide L.

05:30

So let's divide force first.

05:32

So this is F cos 60.

05:34

And this is F sine 60.

05:37

Right?

05:38

So this component of force does not produce torque.

05:40

This component of force produces torque.

05:42

And the torque will be equal to f sine 60 times the this perpendicular distance L.

05:52

Or let's now break L.

05:55

Actually.

05:58

So this is, the door.

06:00

This is F.

06:02

Now I can see like this is the hinge, right?

06:07

So let's extend the direction of this F.

06:10

So this is F.

06:13

So, so this is the perpendicular distance to F.

06:18

Right?

06:18

So, and since this is, What did we Say L L, this angle is 60.

06:24

That means this angle is 60.

06:26

That means this length is L cos 60.

06:30

And the length that we require is L sin 60.

06:34

L sine 60 is the perpendicular distance to the line of action of force.

06:38

So that means torque can be written as f times l sine 60.

06:43

In both the cases the torque will be the same.

06:45

If you want to find the direction of torque because it's a vector, you just have to simply look at the definition again which says R cross F.

06:55

And if you know how to do this, basically it's the right hand thumb rule.

07:00

So R, in this direction you have R, like this and F like this.

07:08

So R, cross F will be this.

07:09

My thumb is here, like coming out.

07:12

So the torque will be coming out of this hinge outward out of the page, okay, towards you.

07:18

So that's how we calculate it using the right hand thumb rule.

07:22

so hopefully that makes you understand torque in depth.

07:26

Okay.

07:27

And just to pitch in at the end, I have a, school community.

07:32

It's on Skoo and you can find this community called AP Physics 5 Club.

07:38

I ask me your questions there.

07:40

It's completely free for the first hundred students.

07:43

So thank you for letting me explain and I'll see you there.

07:45

Take care and I'll see you soon.

Understanding Torque: Line of Action Explained 📐 — Tella