My Math Forum  

Go Back   My Math Forum > Science Forums > Physics

Physics Physics Forum


Reply
 
LinkBack Thread Tools Display Modes
June 13th, 2017, 07:03 PM   #1
Senior Member
 
Joined: May 2015
From: Arlington, VA

Posts: 277
Thanks: 23

Math Focus: Number theory
Two-sphere pendulum

A ball of diameter D, inside a spherical shell of radius D, both with adequate friction at initial contact between equators, act as a pendulum with what period?

Last edited by Loren; June 13th, 2017 at 07:08 PM.
Loren is offline  
 
June 14th, 2017, 04:38 AM   #2
Senior Member
 
Joined: Apr 2014
From: Glasgow

Posts: 2,076
Thanks: 695

Math Focus: Physics, mathematical modelling, numerical and computational solutions
Um... same period as a regular pendulum with a mass equal to the total mass of the ball and shell? Not sure...
Benit13 is online now  
June 14th, 2017, 06:29 AM   #3
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,042
Thanks: 2344

Math Focus: Mainly analysis and algebra
A diagram that illustrates how it acts as a pendulum might be useful.
v8archie is offline  
June 14th, 2017, 07:40 AM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 18,164
Thanks: 1423

Quote:
Originally Posted by Benit13 View Post
Um... same period as a regular pendulum with a mass equal to the total mass of the ball and shell? Not sure...
I think the shell is static, making its mass irrelevant. The question indicates that the ball rolls rather than slips, but without losing energy. Google finds several worked examples of this type of "pendulum", but they don't allow for the large angle of oscillation specified in this problem.
skipjack is offline  
June 14th, 2017, 08:35 AM   #5
Senior Member
 
Joined: Apr 2014
From: Glasgow

Posts: 2,076
Thanks: 695

Math Focus: Physics, mathematical modelling, numerical and computational solutions
Quote:
Originally Posted by skipjack View Post
I think the shell is static, making its mass irrelevant. The question indicates that the ball rolls rather than slips, but without losing energy. Google finds several worked examples of this type of "pendulum", but they don't allow for the large angle of oscillation specified in this problem.
Okay... so the ball with diameter D is rolling around in the inside of a spherical shell with diameter 2D? I guess the period of any oscillations (i.e. rolling up and down the sides of the spherical shell given some initial position away from the bottom) can be determined by building an equation of motion (using Newton's laws) and solving. With friction and the whole rolling/slipping situation, you'll probably get something similar to a damped SHO.
Benit13 is online now  
June 14th, 2017, 09:15 AM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 18,164
Thanks: 1423

Assuming that the shell is hemispherical, one can reasonably assume that the ball starts as illustrated below.
Pendulum.PNG
skipjack is offline  
June 14th, 2017, 04:02 PM   #7
Senior Member
 
Joined: May 2015
From: Arlington, VA

Posts: 277
Thanks: 23

Math Focus: Number theory
Would a two-dimensional, frictionless pendulum simplify the OP (now no slipping)?

The ball would initially be released where the equators meet.

Thanks for the diagram, skipjack.
Loren is offline  
June 15th, 2017, 01:24 AM   #8
Global Moderator
 
Joined: Dec 2006

Posts: 18,164
Thanks: 1423

Do you mean that the ball doesn't "roll" at all?
skipjack is offline  
June 15th, 2017, 09:30 AM   #9
Senior Member
 
Joined: May 2015
From: Arlington, VA

Posts: 277
Thanks: 23

Math Focus: Number theory
I submit two "extremes"; the ball sliding without friction, or the ball rolling with just enough friction to cause it not to slide.
Loren is offline  
Reply

  My Math Forum > Science Forums > Physics

Tags
pendulum, twosphere



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Help with double pendulum using RK4 Rezalt Differential Equations 0 December 18th, 2014 03:26 AM
A pendulum experiment Chikis Physics 6 February 19th, 2013 01:12 PM
pendulum solution msteinma Applied Math 2 June 9th, 2012 10:57 AM
A pendulum+weight problem! Moth Physics 0 October 16th, 2011 07:14 AM
String pendulum jk22 Physics 0 July 7th, 2010 02:26 PM





Copyright © 2017 My Math Forum. All rights reserved.