Consider the simple pendulum: a ball hanging at the end of a string. Derive the expression for the period of this physical pendulum, taking into account the finite sizeball (i.e. the ball is not a point mass). Assume that the string is massless. Start with the expression for the period T'of a physical pendulum with small amplitude oscillatiT= 2πThe moment of inertia of the ball about an axis through the center of the ball isHere, I, is the moment of inertia about an axis through the pivot (fixed point at the top of the string, m is the mass of the ball, g is the Earth's gravitational constant ofacceleration, and h is the distance from the pivot at the top of the string to the center of mass of the ball.Note, this pre-lab asks you to do some algebra, and may be a bit tricky.ImghIball = / mr²T Consider the simple pendulum: a ball hanging at the end of a string. Derive the expression for the period of this physical pendulum, taking into account the finite sizeball (i.e. the ball is not a point mass). Assume that the string is massless. Start with the expression for the period T'of a physical pendulum with small amplitude oscillatiT= 2πThe moment of inertia of the ball about an axis through the center of the ball isHere, I, is the moment of inertia about an axis through the pivot (fixed point at the top of the string, m is the mass of the ball, g is the Earth's gravitational constant ofacceleration, and h is the distance from the pivot at the top of the string to the center of mass of the ball.Note, this pre-lab asks you to do some algebra, and may be a bit tricky.ImghIball = / mr²T

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

Consider the simple pendulum: a ball hanging at the end of a string. Derive the expression for the period of this physical pendulum, taking into account the finite size
ball (i.e. the ball is not a point mass). Assume that the string is massless. Start with the expression for the period T'of a physical pendulum with small amplitude oscillati
T
= 2π
The moment of inertia of the ball about an axis through the center of the ball is
Here, I, is the moment of inertia about an axis through the pivot (fixed point at the top of the string, m is the mass of the ball, g is the Earth's gravitational constant of
acceleration, and h is the distance from the pivot at the top of the string to the center of mass of the ball.
Note, this pre-lab asks you to do some algebra, and may be a bit tricky.
I
mgh
Iball = / mr²
T

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