Main content

## AP®︎/College Physics 1

### Course: AP®︎/College Physics 1 > Unit 3

Lesson 5: Centripetal acceleration and centripetal force# Identifying centripetal force for ball on string

AP.PHYS:

CHA‑4.A (EU)

, CHA‑4.A.2 (EK)

, CHA‑4.A.2.1 (LO)

, INT‑3.B (EU)

, INT‑3.B.2 (EK)

, INT‑3.B.2.1 (LO)

Identifying forces or force components acting as the centripetal force for a ball on a string moving in a horizontal circle.

## Want to join the conversation?

- What about friction in the first example?(8 votes)
- I'm not sure if this is right, so take this as a guess.

Friction acts opposite to the motion of direction. I believe that in this case, the force of friction would be acting perpendicular to the tension force. Because the force of friction acts perpendicularly to the tension force, friction would not be part of the net centripetal force as the force of friction does not act towards the centre of the circle but rather tangentially to the circle, in the direction opposite to the object's motion. Thus, since there is no force acting opposite to the force of friction, the ball would eventually come to a stop.(4 votes)

- At4:19, what happens if the mass on a string is spun so fast that the force of tension only has the x component? What would counter mg?(6 votes)
- since Tension is always parallel to the rope, if you want to spin it faster, you increase the force you apply to the rope F_t. while you're interested in the F_tx increasing, you also increase F_ty which makes your ball go higher (since it is stronger gravity).

the tricky part though: mg does never change on the ball; the ball has the same mass and g is a constant, so what changes? Well, I did say that you increase the ball up, but doing so LOWERS the F_ty force (due to the angle between Ft and F_ty going up 90, which makes F_ty literally 0). A summary is that while you spin it faster, you need to spin it, even more faster to counter the constant mg force.

so this is one of the main reasons you can NEVER spin a ball mid-air keeping the ball as high as your hand, because then the force that counters mg is 0, and then drops down then until F_ty gets some angle(1 vote)

- second example, shouldn't there also be a Fn counteracting Fg, not just the tension force?(3 votes)
- The object is hanging from the ceiling. It is not in contact with the ground. Therefore, there is no normal force.(3 votes)

- I have a question. Please help me understand why don't we have a force that would go in opposite direction from centripetal force? Is it because that one would be applied to the string and not to the object on it?(2 votes)
- Are you asking why we don’t have a centrifugal force? Think about Newton’s first law of motion: an object in motion stays in motion unless acted upon by an outside force. This includes direction; an object will not want to change direction unless it is acted upon by an outside force. So when you have a ball on a string, the ball wants to go straight. It’s the string providing the centripetal force that causes the ball to go in a circular path. We don’t need another force to go in the opposite direction, because that would cancel out the centripetal force, causing no acceleration. That doesn’t make sense, because the ball is accelerating (changing direction, therefore changing velocity)

Let me know if you need more help!(3 votes)

- At4:19how do we know that the vertical component of the force of tension completely cancels the gravitational force? Their might be an additional normal force (which obviously is smaller than the gravitational force in magnitude)!(1 vote)
- We know that the vertical component of the tension “cancels” the force of gravity because there is no acceleration in the vertical (y) direction. Since according to Newton’s second law, ΣF=ma, F_ty + F_g = m*a_y.

a_y = 0 m/s^2

F_ty + F_g = m*0

F_ty + F_g = 0**F_ty = -F_g**

That last equation shows that the vertical component of the force of tension is equal in magnitude, but opposite in direction, to the force of gravity.

There isn’t a normal force because normal force requires contact with a surface. In that second example, the ball on the string is just moving through the air. It’s not on a table.

Does that help?(3 votes)

- 1) In the second example at2:47of a string attached to the ceiling and a ball in the other end of it, in order for the ball to do a circular motion shouldn't we apply an external force?

2) Had we left the ball from that point, wouldn't it move like a pendulum (left and right)?

3) Also, is the force of tension in the horizontal axis called a centripetal force in a pendulum?(1 vote)- 1) When started studying the motion, the ball was already doing a circular motion so no external force was required due to inertia

2) If the ball is at rest and when released then it will move like a pendulum. However as it undergoes circular motion, the tension which would cause it to move left to right is used as centripetal force

3) In circular motion it is a centripetal force(2 votes)

- Isn’t gravity pulling the ball at an angle instead of straight down?(1 vote)
- Are you talking about the second example? If so, the force of gravity always acts downward on an object, toward the earth.(2 votes)

- What about the force that is actually spinning the ball and the friction acting against that force? Wouldn't these two forces work tangentially? Why didn't Sal draw them?(1 vote)
- Will the x component of the tension force always be equal to the centripetal force?(1 vote)
- Anyone taking this as freshmen year Physics>()(1 vote)

## Video transcript

- [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.