Identifying centripetal force for ball on string | AP Physics 1 | Khan Academy

– [Tutor] What we’re
going to do in this video is try to look at as
many scenarios as we can, where an object is exhibiting
uniform circular motion, it’s traveling around in a
circle at a constant speed and what we wanna do is think about why is it staying on the circle, what centripetal force
is keeping the object from just going off in a straight line? So in this first scenario,
I have some type of a wheel, maybe a ball attached to a string, that’s attached to a peg
at the center of the table and this wheel is moving in
a circle at a constant speed, so it’s moving in this
circle at a constant speed, so pause this video, think
about all of the forces that are acting on this wheel
and which of those forces, or maybe some combination of those forces, that are actually acting
as the centripetal force, that are keeping the wheel on the circle. Alright, now let’s work
through this together, so there’s a couple of
forces, that aren’t impacting the wheels staying on the circle
so much, but they’re there, for example, you’re definitely gonna have the force of gravity, we’re assuming we’re dealing
with this wheel on a planet, so we’ll denote its magnitude as capital F sub g and then this is its direction
with this orange arrow, so that’s the force of gravity and the reason why the wheel
is not accelerating downward is that we have that table there and so the table is exerting a normal force on the wheel, that counteracts the gravitational force, so the magnitude there would
be the force, the normal force and these are going to
be the same magnitude, they’re just going to be
in different directions, just let me see if I can draw this arrow a little bit taller, but
what else is going on? Well, as you can imagine,
if this string wasn’t here, the wheel really would
go off in a straight line and eventually fall off of the table and so the string is
providing some inward force, that keeps the wheel going in a circle and that inward force, that pulling force, we would consider that
to be the tension force, so I’ll just draw it like that and its magnitude is F sub T and in this situation, it is
providing that inward force, so that is the centripetal force, so we could say the
magnitude of the tension, the tension force, the pulling force, is going to be equal to
the centripetal force, in this case, they’re actually
the exact same vector, so I can even write it like this, this is the centripetal force vector, it’s the tension in that rope, that keeps us going in a circle. Let’s do another example, so this one is similar, but I have a few more dimensions going on, here this is a classic
example from physics, I have a string attached to the ceiling and I have some type
of a ball or a pendulum and it’s swinging in a
circular, in a circular motion right over here at a constant speed, so the center of its circle
would be right around there, so once again pause this video, think about all of the forces on that ball and we’re not gonna talk too
much about air resistance, let’s assume that these are
in vacuum chambers for now and then think about,
well, which of those forces is providing the centripetal force? Well, just like in the last video, there’s definitely some force of gravity, so you have that vector right over there and so its magnitude is F sub g and you also have the
string holding up the ball and so you’re gonna have its pulling force on, so this would be… the magnitude here would be F sub T, this is the tension force, but what’s counteracting the gravity and what’s keeping us going in a circle? Well, in this situation,
we can think about the different components of the tension, because this is going off at an angle, so if we break down that vector
in the vertical direction, so if we take the vertical component, or the y component of the tension force, it would look something like this, we could call that F Ty for the y component, this
would be its magnitude and that is what is
counteracting the gravity, why the ball is not accelerating downwards and if we think about the
x component of the tension, that would be this right over here, this is the x component of the tension, just to be clear where
I’m getting this from, so this would be F tension
in the x direction, that would be its magnitude and that is what is providing
the centripetal force or that is the centripetal
force, so in this situation, the component of our
tension in the x direction and let me just denote that as a vector, that is our centripetal force, that’s what keeps the ball from just going straight off
in a direction like that.

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