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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).
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
Full Transcript
- 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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