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## AP®︎/College Physics 1

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

Lesson 6: Free-body diagrams for objects in uniform circular motion# Identifying force vectors for pendulum: Worked example

A worked example finding all force vectors acting on a pendulum moving in a horizontal circle.

## Want to join the conversation?

- Shouldn't the answer be D? He never mentioned that the air resistance was absent, and air resistance would push the ball in the opposite direction of its velocity as shown in the leftmost arrow of choice D.(6 votes)
- Usually for pendulums we ignore air resistance because the math would be too complicated.(7 votes)

- What about the normal force acting on the ball? Is it equal to the y-component of the force of tension or is the force of gravity equal to the sum of the magnitudes of the y-component of tension and the normal force?(1 vote)
- The normal force itself is the force of tension. The ball wants to go in outwards direction so it actually pulls the string. The normal force that the string applies on the ball is the force of tension we are talking about.(4 votes)

- Is there centripetal force for pendulum-type structures? Why or why not?(2 votes)
- Yes, there is. When a pendulum is moving it is traveling at a speed in a path that is a section of a circle. Therefore, there must be a centripetal force. Note, that through the pendulum's path, the magnitude of the force changes due to the fact that the speed of the pendulum changes.(1 vote)

- Why did not we choose D as there is a centrifugal force to the left?(0 votes)
- This is a very common misconception. There is no such thing as a centrifugal force. This is a fictitious force. The reason why it looks as if such a force exists is because of the objects inertia. When you are getting something to move in a circle, you are constantly changing its direction, but the object's inertia causes it to want to continue in a straight line. This resistance to a change in its motion is what looks like a centrifugal force but its really just inertia. Therefore, D cannot be the answer as no such force acting towards the left exists. Hope this helps!(3 votes)

- I have some doubts...when do we use centrifugal force? and what happens when there is friction...how does it affect the motion?(1 vote)
- Wait... Why isn't the answer "D"? Won't there be Air Resistance? He never mentioned that the place is vacuum.(1 vote)
- The question states constant speed meaning the ball isn't slowing down and therefore cannot be subjected to air resistance.(1 vote)

- just.....but aren't components also forces? @2:13(1 vote)
- image is on 3D not 2D right? and ,the ball is moving is 3D right? yeah because you can see an arrow in the image that looks like rotation on the x and z

if so then why only 2D arrows....(0 votes)- I think that what you're asking is why there is only a down arrow and a diagonal arrow without respect to 3 dimensions. These two arrows are the only forces acting on the object (neglecting air resistance because in physics there is never air resistance unless specifically stated). Since from our point of view, the ball is hanging out to the side as far as it can reach in the circle, the force of tension (diagonal arrow) is at the same angle as the string. It is the same as a drawing of a cone: The edges appear to meet at the tip and meet a curve at the bottom, but as a 3d cone object these edges don't exist, they are just a point on the face of the cone. And gravity is always straight down no matter where you are.(1 vote)

## Video transcript

- [Lecturer] We're told that
a ball attached to a string swings in a horizontal
circle at constant speed as shown below. The string makes an angle
theta with the horizontal. Which arrows show all
the forces on the ball? So pause this video, and see
if you can figure that out. Okay, so let's work through this together. So this ball is attached to the string, and it's currently hanging down, and I think it's fair to say that we are on some type of a planet. And so, if we're on some type of planet, you're definitely gonna
have the force of gravity acting on the ball, so
let me draw that vector. So the force of gravity,
I'll do in orange. Let's say it looks something like that. Its magnitude, I'll denote as capital F with a sub g right over here. Now what's keeping that ball
from accelerating downwards? And also, what's keeping that ball in this uniform circular motion? And the answer to both of those questions is the tension in the rope. Remember, tension is a pulling force. The rope is pulling on this ball. And so, we could say the force of the tension, so it might
look something like this, the force, force of the tension. Now just with that, we have
constructed a free body diagram, and we can immediately
answer their question, what are the forces that
are acting on the ball, which arrows show it. So there is one downwards, and then there is one going in
the direction of the string, and if you look at these choices here, you would say it is that
one right over there. Now some of you might say,
"Wait, hold on a second. "Isn't there some type
of a centripetal force "that keeps the ball going in a circle, "that keeps it from
just going straight off? "And then isn't there some type of force "that counteracts the
actual force of gravity?" And the answer to the
question is yes, there is but those are really just
components of the tension. And so, if you look at the
X component of the tension, I'll do that in a blue
color right over here, this X component of the tension, so I'll call that F sub Tx,
that is our centripetal force, or that its magnitude of
the X component of tension is the same thing as the magnitude
of our centripetal force. If we look at the Y
component of our tension, the Y component of our tension, that's what counteracts
the force of gravity. So this right over here,
its magnitude is F sub Ty, and F sub Ty, this magnitude
is going to be the same thing as the magnitude of the force of gravity. But we already answered our question, and we just got a little
bit more intuition of what's going on right over here.