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Physics Videos 34 videos

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Physics: Circular Motion 63 Views


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Description:

In this video, we'll cover inertia, centripetal force, circular motion, and what Newton liked to eat for breakfast in the morning (Apple Jacks).

Language:
English Language
Subjects:

Transcript

00:03

circular motion round and round around we go where we stop

00:06

well physics probably knows....

00:30

Well when you do crazy things [Man flying a plane]

00:36

at an airplane it's good to have a decent understanding of physics like

00:39

when you're flying upside down it's helpful to understand what you need to

00:43

do to counteract the acceleration of gravity otherwise landing the plane [Plane landing upside down]

00:47

could come a bit you know earlier than you were hoping for a bit rougher - same

00:53

thing if you're gonna pull off a perfect loop-de-loop well you've got to know

00:57

what's creating your centripetal force so you know how to make it work in your

01:02

favor because no one likes a loop-de-loop that turns out to be a [Plane crashes into the floor]

01:07

know loop-de-crash especially the pilot so how does circular motion really work

01:12

well the key thing is centripetal force that's the force that's able to overcome

01:16

an object's inertia and create the circular motion well it turns out [Plane travels in a circular motion]

01:21

there's a handy little equation for centripetal force and it's this one

01:25

right here this equation says that centripetal force F sub C equals mass

01:31

times the square of the object's velocity divided by the radius of the

01:37

circle got it okay and this works for whatever the centripetal force is

01:41

whether that's tension, gravity or you know whatever and which comes in handy

01:46

when we know the equation for whatever type of centripetal force we're dealing [Equations for types of centripetal force]

01:50

with if the centripetal force is a friction

01:54

force for example we know that the equation for friction is the coefficient

01:57

of friction times the normal force so we have two equations for the same force we

02:03

set them equal to each other and use them to find values for unknown

02:07

variables now one of the basic laws of physics is that force equals mass [Formula for force]

02:12

times acceleration well Isaac Newton dropped his three laws of motion way [Isaac Newton underneath a tree]

02:16

back in 1687 and this equation was the basis of law number two because of this

02:23

law we can say that centripetal acceleration equals velocity squared

02:28

over the radius why well because everything is contained in the force

02:33

equation except the mass and there is always acceleration when it comes to [Moon orbiting the Earth]

02:38

circular motion even when the velocity is constant

02:42

remember velocity is the rate of displacement over time and it's a vector

02:48

quantity so it has both a magnitude and a direction acceleration is the rate of

02:52

change in velocity over time and in circular motion even if the magnitude of

02:57

velocity stays the same, the direction is constantly changing which means there's

03:03

constant acceleration even when the speed stays the same it's kind of like a

03:08

trick question of nature....

03:11

yeah circular motion can definitely make your head spin [Mans heading spinning in circular motion]

03:14

Now all this time we've been talking about centripetal

03:18

force like it's just one thing but there can be more than one force creating the

03:23

total centripetal force say we're planning with one of these cool toy [Man holding toy airplane]

03:27

airplanes well we tie some string around it and

03:30

spin it around vertically and wee boy! this is fun who needs an Xbox but let's

03:35

freeze it here at the top all right at this point what is the centripetal force [Airplane frozen at the top of the circular motion]

03:40

well we've definitely got tension on the string otherwise the toy plane here

03:44

would just keep going parallel to the ground so the tension on the string is

03:49

pointing to the center of the circle like any centripetal force does but

03:53

there's another force pointing that way too that would be our old pal gravity so

03:58

gravity and tension are working together to create the centripetal force in fact [Gravity and tension merge together]

04:02

we could even write this as an equation like this one - gravity plus tension

04:07

equals mass times velocity squared over the radius it's the opposite situation

04:12

when the plane is at the bottom of the circle here tension is pulling up toward [Arrow showing tension pulling upwards]

04:18

the center of the circle but gravity is still pointing down which means it's

04:23

pointing away from the center it's like a bad relationship you know

04:27

one minute they're working together the next they're in complete opposition and [A man and woman cuddling]

04:30

it just keeps going in circles and so at the bottom of the journey the equation

04:34

for centripetal force looks like this tension - gravity equals that

04:40

centripetal force equation which means that the tension in the string is having [Man holding a string]

04:44

to do a lot more work at the bottom of the circle than it is at the to

04:48

Now that we have some equations to work with we can start doing some actual

04:51

math... well back when I was just a little co-pilot my favorite thing at [Young boy wearing pilot gear at playground]

04:57

the playground was the merry-go-round you'd get that thing spinning so fast it

05:02

felt almost like flying... so let's say I put my son on one of these

05:06

contraptions he loves it the kiddo has a mass of 10 kilograms and [Son stood on a merry-go-round]

05:11

I get this thing spinning at a velocity of 5 meters per second it's pretty fast

05:16

if the radius of the merry-go-round is 5 meters

05:20

What's the kid's centripetal force and the centripetal acceleration....

05:25

well let's start with the centripetal acceleration since that's a component of

05:29

centripetal force like we've got to get that number first well the equation for

05:33

this acceleration is velocity squared over the radius and with a velocity of 5

05:38

meters a second and a radius of 5 meters we come up with an acceleration of 5 [Formula for son's centripetal force]

05:43

meters per second squared to find the amount of force we can just multiply the

05:47

acceleration by the mass which was 10 kilograms making the force 50 Newtons

05:52

hope the little tyke holds on tight there well flying yeah is in his blood [Boy falls off the merry-go-round]

05:57

Well after I convinced Jr. to basically never tell his mom about this

06:03

we'll head off to get some ice cream yeah...The landscape around here is a

06:06

little weird lots of hills and valleys in there almost like half circles well [Car on top of a hill]

06:11

let's draw a force diagram for the car at the top of the hill and the bottom of

06:14

the valley all right then we can figure out what our centripetal force equations

06:18

would look like okay here we go so let's start at the top so we're in a moving

06:23

car which means we have the applied force from the engine pushing us forward

06:26

and friction is pushing in the other direction and how about along the y axis

06:30

well there's definitely gravity in the normal force to deal with but are they

06:35

equal or is one bigger than the other this is circular motion here people so [Circular motion appears at the top of the hill]

06:41

there has to be a centripetal force the center of the circle is straight down

06:45

and guess which direction gravity works yeah, that's our centripetal force

06:50

but we've also got the normal force of the road pushing up because we're

06:55

continuing in our circular motion there has to be acceleration right and in

06:59

order for there to be acceleration well we have to have a net force. If the

07:03

forces were equal in the net force was zero our motion would continue in the [Car flys across the hills]

07:07

direction of the velocity vector and we'd be catching air on this hill with

07:12

the tyke in his car seat back there I figure I should take it easy [Man in the car with his son in the backseat]

07:16

you know the straps aren't that tight...So gravity has to be stronger than the

07:20

normal force here we'll show that on our diagram by making the gravity arrow

07:24

longer than the one for normal force - now when we're at the bottom of the hill in [Car travels to the bottom of the hill]

07:29

the valley here the situation's reversed we've still got our applied force and

07:32

our friction but now the center of the circle is straight up just like the

07:36

normal force and the normal force has to be greater than gravity so it'll get the

07:41

longer arrow this time well you might have experienced this exact same thing [People riding a rollercoaster]

07:45

on a roller coaster think of going down that first big hill well at the bottom

07:50

you're pressed hard down into the seat that's because your inertia and gravity [Arrows point to inertia and gravity of people on a rollercoaster]

07:54

are working in similar directions your body wants to keep going in the same

07:58

downward angle of the hill and gravity is pushing you straight toward the

08:02

ground so as you're being pushed down harder into your seat your seats pushing

08:07

back up onto you with equal force so now all we have to do is figure out the [Car travels up the hill]

08:13

equations for centripetal force at each point in our ice cream trip... At

08:19

the top gravity minus normal force equals centripetal force and at the

08:23

bottom it's normal force minus gravity and at the ice cream shop it's vanilla [Man in the car at the ice cream store]

08:28

plus brownie fudge equals young yeah now sometimes Jr. gets bored so I

08:33

brought along that plane on a string that I was playing with earlier well [Man gives Jr a toy plane]

08:36

hopefully that'll keep him distracted long enough for me to finish the rest of

08:39

his frosty treat as he's swinging the plane around vertically let's do [Jr swining plane in garden]

08:43

something different at the top of the circle the plane has a velocity of 3

08:46

meters a second it has a mass of 0.5 kilograms and the force of tension on

08:51

the string is 15 Newtons let's put those numbers into a centripetal force

08:55

equation and use that to find the radius of the circle hmm well this is gonna be

09:00

a little trickier than what we've had to do before but it's nothing we can't

09:03

handle we have the toys mass and its velocity and we know the tension force

09:07

but we can't just plug all that into the centripetal force equation and solve for

09:12

R because tension isn't the only force that's in play here. At the top [Jr holding toy plane on a string and gravity line appears]

09:17

of the circle we've got gravity to factor in too - so our centripetal force

09:21

equation will be gravity plus tension equals mass times velocity squared over

09:26

the radius well since F sub G equals mass times the

09:30

acceleration of gravity we can sub in those variables the equation gravity

09:35

probably hasn't changed in the last few minutes so it's still 9.8 meters per

09:38

second squared multiplying that by point five kilograms gives us a force of

09:43

gravity of 4.9 Newtons and now we can plug in the numbers and find the radius

09:47

well 15 Newtons plus 4.9 Newtons equals 0.5 kilograms times the square of 3 [Formula to find the radius on a board]

09:54

meters per second over R when we do that first bit of addition, well we get

09:59

19.9 Newtons and rearranging that equation to solve for R [Equation rearranged to solve for R]

10:03

we find that R equals 0.5 kilograms times the square of 3 meters per second

10:08

over 19.9 Newtons and Mr. calculator tells us that the radius then

10:12

equals 0.23 meters it's a pretty tight turn there but we've got to use the

10:18

right amount of significant figures so the radius is 0.2 meters not

10:22

very big but big enough to do damage and that's what happens when you lose your [Boy swining toy plane on a string]

10:27

centripetal force okay time to go it's important to recognize when there are

10:32

two forces in action that are combining to create centripetal force or when

10:37

they're in opposition with one creating the centripetal force and one acting

10:41

against it and real life isn't always just up or down there might be times

10:45

when we have to break a diagonal force vector into x and y-components but we [Blue ball travelling in circular motion]

10:51

have all the skills now to handle that and even if we crash and burn on a

10:54

physics problem well there are worse ways

10:57

to crash and burn.. [Man parachuting down to the ground]

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