# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sat, 18 May 2013 11:42:11 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 2 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: energy in rotational motionPosted: Sun, 22 Jun 2003 08:17:29 UTC
 Member

Joined: Sat, 21 Jun 2003 15:48:20 UTC
Posts: 23
Four small spheres, each of which can be regarded as a point of mass 0.200 kg, are arranged in a sphere 0.400 m on a side and connected by light rods. Find the moment of inertia of the system about an axis:
a.) through the center of the square, perpendicular to its plane (an axia through point O in the figure;
b.) bisecting two opposite sides of the square (an axis along the line AB in the figure);
c.) that passes through the centers of the upper left and lower right spheres and through point O.

Top

 Post subject: Posted: Mon, 23 Jun 2003 02:48:25 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 22 Jun 2003 18:00:06 UTC
Posts: 3461
Location: North TX
For a point mass, the moment of intertia, I = m*r^2, where m is the mass of the object and r is the distance of the mass from its center of rotation.

I assume you meant that all four masses are arranged in a square.

a. Each mass is 0.4/sqrt(2) m from the square's center.
I{system} = 4*m*r^2
I = 4(0.2 kg)[0.4/sqrt(2) m]^2
I = 0.064 kg*m^2

b. Each mass is 0.2 m from the axis of rotation
I = 4(0.2 kg)(0.2 m)^2
I = 0.032 kg*m^2

c. Only two masses (upper right and lower left) will affect the rotational inertia since the axis of rotation passes through the upper left and lower right masses (their radius = 0). Those two masses are at a distance
r = 0.4/sqrt(2) m from the axis of rotation.
I = 2*(0.2 kg)[0.4/sqrt(2) m]^2 = 0.032 kg*m^2

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous