Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Prove that the centroidal polar moment of inertia of a given area $A$ cannot be smaller than $A^{2} / 2 p .$ (Hint: Compare the moment of inertia of the given area with the moment of inertia of a circle that has the same area and the same centroid.)

Get the answer to your homework problem.

Try Numerade free for 7 days

Input your name and email to request the answer

Like

Report

Think about what shape can have a certain area while minimizing the polar moment of inertia and calculate it using equation 9.3.

Physics 101 Mechanics

Chapter 9

Distributed Forces: Moments of Inertia

Moment, Impulse, and Collisions

Rotation of Rigid Bodies

University of Michigan - Ann Arbor

Hope College

University of Sheffield

University of Winnipeg

Lectures

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

15:07

Prove that the centroidal …

03:05

Determine the polar moment…

No transcript available

View More Answers From This Book

Find Another Textbook

02:54

If the length and breadth of a rectangular sheet one measured to be 5.7cm an…

01:26

Determine the frequency of a microwave 6.0 cm in length. (a microwave is an …

01:10

10 cm x 5 cm x 2 cm and has a mass of 1,930 g. What is the density of the go…

03:08

3. A force F = (3xN)i +(4N)ſ, with x in meter, acts on aparticle, changing o…

01:44

An object accelerates uniformly along a straight track with acceleration of …

02:37

to prevent rusting a layer of ______ metal is applied on iron sheets

00:35

1o. Discoveries in physics generate new technology. Give an evidence to this…

01:32

Shreya amused her friends by sticking balloons to the wall by just rubbing t…

02:31

3. Collect information about importance of the pH value in daily life to hum…

01:03

Two blocks of lead, one twice as heavy as the other, are both at 50 degree c…