### Torque: Crash Course Physics #12

You have a box. A ring. And a marble. And they’re all at the top of a ramp. Because

you know how physics loves ramps. Especially hypothetical ramps! So, let’s say this ramp would allow for static friction, but not kinetic friction. Now, you let go of all of these objects at

the same time, so that the box starts sliding, and the ring and marble start rolling, all

at once. So, which of them will hit the bottom first? The answer might not be what you’d expect. I mean, we already know that when you drop

two objects from the same height — in a vacuum at least — they’ll hit the ground at the same time. Even if you tried it with a feather and a bowling ball. So you might think that all of the objects

would get to the bottom of the ramp at the same time. But they won’t. The reason has to do with how energy is distributed

in an object when it’s rolling. And in order to understand who wins the ramp-race, and why, we have to investigate some qualities of rotational motion: Specifically, torque, and the moment of inertia. [Theme Music] Have you ever tightened a bolt with a wrench? Or pulled a door open?

Me too! When we do those things, the wrench and the

door’s handle do their jobs using torque. That is, they apply a force perpendicular to the axis of rotation, which makes the bolt turn and door swing open. That’s what torque does — it makes things

rotate faster or slower. In other words, torque changes an object’s

angular velocity. For the first few weeks of this course, we described net forces as changing an object’s linear velocity, how fast it moves through

space, and in what direction. Torque essentially does the same thing, but

for rotational motion. This means that a lot of the relationships and equations that apply to forces will apply to torque in a similar way. But first, let’s talk about how to calculate torque, by analyzing what happens when you open a door. The harder you pull on the handle, the more torque you’ll generate, and the more you’ll change the door’s angular velocity. More net torque then, means the door

starts moving faster on its hinges. So, the strength of the force that’s applied

is one factor that affects torque. Another is the distance between the force

and the axis of rotation — or the radius. A larger radius means more torque. You know this if you’ve ever tried opening a door with a handle that’s too close to the hinge. I’m guessing you haven’t tried

that, though, because there’s a reason doorknobs are generally placed far from the hinges. A door with a handle close to the hinges would

be much harder to open, because you get less torque for the same amount of force. The last factor that affects torque is the

ANGLE BETWEEN the applied force and the radius. If you tried to open the door by pulling the

handle, say, parallel to the door — in the direction opposite from the hinges —

the door wouldn’t move. Because the only part of the force that affects

the door’s rotation is the force that’s Perpendicular to the radius. To put this idea in mathematical terms, torque

— represented by the Greek letter tau — is equal to the perpendicular force, times the

radius. And, you know how we keep saying that for

translational motion, a net force on an object is equal to its acceleration times its mass? Well, something similar applies to rotational

motion, too: The net torque on an object is equal to its angular acceleration, times what’s known as its moment of inertia. Now, we’ve talked about inertia before,

at least as it relates to translational motion. Basically, it’s an object’s tendency to

keep doing what it’s been doing. An object with lots of inertia is harder to speed up or slow down. And in translational motion, the inertia of

an object depends on mass. The MOMENT OF INERTIA works in a somewhat

similar way for rotational motion … but the best way to define is mathematically. Specifically, the moment of inertia is the

sum of all the individual points of mass in an object, times the square of their distance

from the axis of rotation. So, much in the same way that inertia relates

to an object’s mass in translational motion… … the moment of inertia relates to mass,

too, but it depends on how that mass is distributed. The farther away the mass is from the axis

of rotation, the higher the object’s moment of inertia. It’s possible to derive the equation for

an object’s moment of inertia, by integrating the square of the object’s radius over its mass. But those integrals can get complicated. So this is one of those rare cases where,

if you’re asked to solve problems using moments of inertia and you don’t have access

to the equations, it’s probably worth memorizing them. Now, there’s another thing that torques

and forces have in common, and it’s going to be the key to figuring out which object wins the race down the ramp. Namely: torques, like forces, have the ability

to do work. As you might remember from our episode on

work and energy, the work done by a force is just the integral of that force over a

certain distance. In a similar way, the work done by a torque

is the integral of that torque over a certain angle. Meaning: the more torque you apply while rotating

an object, the more work you do. We also know that work changes the

energy of a system. For example, it can change its kinetic energy, which is the energy of its motion. In the case of objects that move without rotating, all of that kinetic energy goes into translational motion. In this case, keep in mind that — as we’ve

gone over before — the kinetic energy of translational motion is equal to half of the

object’s mass, times its velocity squared. But when an object is ROTATING, some of its

kinetic energy is also taking the form of Rotational Motion. And calculating the kinetic energy of rotational

motion is pretty easy. Because, first, the moment of inertia affects rotational motion in the same way that mass affects translational motion. And second, rotating objects have angular

velocity, just as translating objects have linear velocity. So, the kinetic energy of an object’s rotational motion is just half of its moment of inertia, times its angular velocity squared. OK, there’s just one final factor we have to consider, before we finally get back to the box, the marble, and the ring racing down the ramp: And that factor is angular momentum. We’ve talked about linear momentum — and

how it’s equal to an object’s mass times its velocity. Well, there’s also angular momentum, which is equal to an object’s moment of inertia times its angular velocity. And, like linear momentum, angular momentum

is always conserved. That’s another one of those super-fundamental principles of physics: You can’t create or destroy angular momentum. It always has to go somewhere. So, now, let’s get back to The Great Crash

Course Physics Ramp Race. All three objects — the box, the marble,

and the ring — are covering the same distance. And what we want to know is, how fast do they

cover that distance? The answer has to do with what happens to

each object’s energy as it moves down the ramp. When they’re at the top of the ramp, all the energy of each object takes the form of gravitational potential energy, which is equal to the object’s mass, times small g, times the height of the ramp. As they move down the ramp, all of that potential

energy gradually gets converted into kinetic energy. In the case of the box, all of its potential energy will be converted to translational kinetic energy, because that’s the only

kind of motion it has. So the object that gets to the bottom of the ramp first is … the box! Because, for both the marble and the ring, some of their potential energy gets converted into rotational kinetic energy. And energy that goes into their rotation isn’t

being used to make them move faster down the ramp. So really, anything that slides — at least

on our hypothetical ramp with no kinetic friction — will reach the bottom before anything that

rolls. And the masses of the objects don’t even

matter, because the energy of an object with more or less mass will increase or decrease

accordingly. So, the box wins. But what’s the runner-up? Does the ring reach the bottom next, or does

the marble? That question is a little more complicated, but it turns out that the marble reaches the bottom before the ring, because it has a lower

moment of inertia. The marble is a solid sphere, so its mass

is distributed closer to its center. But the ring’s mass is distributed in a,

well, ring — so its mass is distributed far from its center, giving it a higher moment

of inertia. What does that mean for the marble’s speed

versus the ring’s? Well, since the marble has a smaller moment

of inertia, its velocity can take up a larger proportion of its kinetic energy — which

means it moves faster down the ramp. So, the final results of the race? The box wins, the marble comes in second,

and the ring finishes last. Today, you learned about torque, and how it

relates to an object’s angular acceleration and its moment of inertia. We also talked

about how to calculate moments of inertia, angular momentum, and the fact that torques

can do work. Finally, we figured out what would happen if you let a box, marble, and

ring move down a ramp. Crash Course Physics is produced in association

with PBS Digital Studios. You can head over to their channel to check out amazing shows

like PBS Idea Channel, Blank on Blank, and Physics Girl. This episode of Crash Course was filmed in

the Doctor Cheryl C. Kinney Crash Course Studio with the help of these amazing people and

our equally amazing graphics team is Thought Cafe.

Keep on rolling

I feel like she’s trolling me. I hate her

That's not a marble… that's a Dragon Ball lol

quite a marvelous marble

"with No kinetic friction" ……..

hve been 2 years

Did she give a lecture or she read out the lecture? How is it possible to continuously give a lecture like this?

U explaination is awesome my mind blows up

Note that the ramp is frictionless. If the ramp had friction, the marble and ring would likely get down faster (specifically, the marble) because rolling friction is less powerful than static/sliding friction. That said, the example is meant to illustrate how torque and conservation of energy work, so mentioning friction would be counterproductive to the video.

These videos suck because of the indian girl. Shes gross to look at, and has a disagreeable accent. Great potential lost in the name of diversty.

I feel a strange torque in my pants

This video gets real, quick.

Too fast to keep up..

Watch it in 2× speed..lmao

so shitty! seems like just reading from wikipedia. no insights, just pure facts

My head has blown up, I wanna cry, and my acne is back after watching one video

I unfortunately haven't yet studied calculus, is there another law for torque?

she reminds me of symmetra from Overwatch

LMFAO DRAGON BALL IN THE FIRST FRAMES

Maaaaaan she never stops

tourqing

So beautiful

when she torque, she knows what she Tolkien about.

"me too!" – I died

Moar torque lessons

At 5:07, there is an error. The bottom part is suppose to say "rotational motion", not "translational motion".

Will you marry me?

Wouldn't the ball fall faster due to increase amount of mass rather than the feather @ 0:28

thanks…im finally read for my test tomorow

Can someone tell me why all the masses cancel out???

can u calculate how many words u say in a second

Take a breath lady…You explained it amazingly! Thank you so much crash course now I understood the torque😍

Linear momentum is the product of moment of inertia and the angular velocity if and only if the axis of rotation of that body is a principle axis

this narrator has too much torque. slow TF down

DRAGON BALLLLLLLS

2:15 In a hole in the ground , there lived a Hobbit.

6:57 One ring to bring them all , one ring to find them all , One ring to rule them all.

Hey I think crash course should do a episode on tension please…. Do it I can't understand it and you explain really nice

Just listen to James Charles for practice listening to her

I think after our school new curriculum I understand a lot of what she is saying , but she is better at explaining it than my teachers 😂😂😂

Wow she can hold her breath for 8 mins straight

I am sorry, but how would the box get down before the ball or the ring? We already assumed that the surface is frictionless and so there would be no friction force that would cause the ring, or the ball, to rotate. Therefore, there would be no loss( or transformation) of potential energy to rotational energy of either the box or the ball.

…apart from physics.. i love her eyes..

6:27 you mean kinetic energy of rotational motion.

2:17 HAHAHA

I hate to say this but – if there's no kinetic friction, surely the ring and marble wouldn't actually roll, but would slide.

why a dragon ball though?

Talks a bit fast for me

6:27 a little mistake!

great

To those taking high school Physics, you will still be talking about this in University Physics. To those in University Physics, you will still be talking about this in Dynamics.

These videos are incredible. They are really helping me with my college course. Thank you! 🙂

So why did the box make it to the bottom first??

Wait, but if there is friction to keep the ring and the marble from slipping, there's friction applied to the box, and rotational friction is wayyy lower than the box. I get the situation she sets up is such that once the box starts moving, it loses all friction. However, the situation is difficult to conceptualize. A surface upon which friction is zero when things start to move. Otherwise, it's a great review for moments of inertia. Might be good to go through some of the derivations as well.

I barely understand what she says. Can we have a speaker with an American accent plz? AP is for Americans therefore, AP students need to understand an accent they are accustomed to…

So, what is the difference between torque, angular momentum and moment (as you often hear in engineering). All of them seems to have the same definition i.e. force x distance.

Hey CrashCourse………Who is this beautiful South Indian lady? She can instruct me any time.

Don’t get anything

Like charlie puth says " We dont torque anymore ~"

"you know how physics loves ramps, especially hypothetical ramps" , please tell me something more true than this

Hit like if you want the blonde guy back . This girl doesnt know how to explain thank god they have animations so we can understant from it not from her

You speak very fast and hard to understand.

Only a car enthusiast will understand what Torque is

I’m fully distracted here 🥴😍

You make it worse

SHe is faster than the speed of light

@5:05 Should it not be "kinetical energy of rotational…" in the bottom equation ?

Great video!

If you feel she speaks fast , then see in 0.75x speed you will understand properly

I think i'm in love

what a beauty

she looks inhuman

creeps me out

Thanks a lot mam 😊 . You are awesome

Im so confused rn. So why did she particularly use static friction. Also i cant see the objects rolling, why would the energy be used? The bottom most point is just sliding wrt the wedge. Shouldnt this be kinetic friction

Why did she use static friction and not kinetic friction?

to everyone saying that she is talking really fast.. that is because (if you haven't noticed) the channels name is called crash course and hence they have to explain topics quickly. I think that these videos are like reference materials that you can use to understand concepts quickly once you have a brief idea of the concepts.

Only nerds and car enthusiasts understand this video

Works better at ×0.75 speed

this video was very helpful, thanks guys

I like the way she torques

Thanks for helping me out with class 11 physics . Exam tomorrow

I just spent 5 minutes of my life opening and closing my door at difference angles and lever arms

She spoke like a speedy truck passing by honking continuously… Now I need to look for another video.

I think I am in love

damn gurl your very prety

ya but we forgot to calculate for the potential energy when you collect all the dragon balls, at which point anything becomes possible including winning the race

Stinky A level physics doesnt teach this

This helps a lot, just what I need for exam review!

Hehake! Slow down msizo

Loved the video but in the case of the ramp, I'm pretty sure that friction between the box and ramp is kinetic, there is relative motion B/w the two surfaces..

Thank you for helping me through my physics assignment. Great video!

The ramp example is flawed. For rotational energy to be taken into account, friction must exist to make the ring/marble spin. If the object make contact with a 0 friction surface, they cannot engage in spinning, they would just slide down the ramp.

She teaches me in a very good manner and when I become board I speed up the vedio and slow down it it's really fun

…

I love how they used the ring from Lord Of Rings to explain physics 😂😂😂😂

But without kinetic friction how is the box moving?

I'm learning my whole semester in one day

So is torque a pseudo vector in the direction of the pseudovector of angular velocity?

Two LotR references in Physics? I approve

Inertia is resistance…