Rotational Motion: The Relationship Between Linear and Angular Displacement

Thread starter ehabmozart
Start date Jan 1, 2013
Tags

Motion Rotational Rotational motion

AI Thread Summary

In rotational motion, when a mass attached to a rope falls a distance x meters, the string must also move through x meters around the rim or disk. This relationship can be expressed mathematically as s = rθ, where s is the linear displacement, r is the radius, and θ is the angular displacement in radians. The discussion emphasizes that the linear distance fallen by the mass directly correlates to the angular distance traveled by the rim or disk. This connection highlights the conservation of distance in the system. Understanding this relationship is crucial for analyzing rotational dynamics effectively.

Jan 1, 2013

ehabmozart

Suppose a mass attached to a rope which winds around a rim or a disk. If the mass attached to the string falls x meters, should the string also move thorugh x meters around the rim or the disk which we can relate by s = r theta?

Physics news on Phys.org

Jan 1, 2013

HallsofIvy

Science Advisor

Homework Helper

Yes, it pretty much has to doesn't it? That "x" distance has to come from somewhere!

Thread 'Is calling fictitious forces "not real" just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...

View full post »

Thread 'Inclined treadmills and Galilean Invariance'

This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/

View full post »

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

View full post »