Pendulum Projectile: Find Direction of Travel Formula

AI Thread Summary
The discussion revolves around determining the direction of travel for an object released from a pendulum when the string breaks. It is noted that if the string breaks at the lowest point, the object will move horizontally, while breaking at a 90-degree angle results in vertical motion. The conversation highlights the confusion regarding calculating the angle of the tangent line in relation to the pendulum's motion and gravity. Participants clarify that the path of a pendulum is not circular, emphasizing the need to understand the geometry involved. Ultimately, a deeper understanding of the pendulum's mechanics and geometry is necessary to accurately determine the direction of travel.
Jrlinton
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Homework Statement


This isn't a specific problem, I just wondering if there was a formula to describe the direction of travel an object would take if it was part of a pendulum and the string broke.

Homework Equations

The Attempt at a Solution


Seeing that if the string broke in the instant that the object was in its most downward position it would be released at an angle parallel to the horizontal and of it broke when the object was exactly 90 degrees from the resting position, it would travel straight up/down depending on where it was in its period, I would think that the direction of travel would be the tangent of the curve at that position? Is there is simplified equation for this?
 
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Jrlinton said:
would be released at an angle parallel to the horizontal and of it broke when the object was exactly 90 degrees from the resting position, it would travel straight up/down
You've got the hard part; the rest is ballistics.
 
Okay I guess what I'm confused about is how to find the angle of the tangent line in relation to the axes in a situation like a pendulum where the axes are dictated by gravity. So how would one find the angle of a tangent line and the origin as it relates to the position of the bob in motion.
 
So in other words the angle of the velocity and the horizontal.
 
Jrlinton said:
how would one find the angle of a tangent line
Is there a difference between the geometry of a pendulum and that of a circle?
 
I understand that. I guess my knowledge of circles is sub par. After drawing it up and unconfindently using what I could recall from geometry I figured the angle was equal to that of the angle between the position of the bob to the vertical?
 
How about "perpendicular to the radius?"
 
Bystander said:
Is there a difference between the geometry of a pendulum and that of a circle?

The path of a simple pendulum is not a circle
 
lychette said:
The path of a simple pendulum is not a circle
:wideeyed::nb):wideeyed::nb):wideeyed:
 

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