Download presentation

Presentation is loading. Please wait.

Published byIndia Southern Modified over 2 years ago

1
Moment of Inertia

2
Moment of Inertia Defined The moment of inertia measures the resistance to a change in rotation. Change in rotation from torqueChange in rotation from torque Moment of inertia I = mr 2 for a single massMoment of inertia I = mr 2 for a single mass The total moment of inertia is due to the sum of masses at a distance from the axis of rotation.

3
Two Spheres A spun baton has a moment of inertia due to each separate mass. I = mr 2 + mr 2 = 2mr 2 If it spins around one end, only the far mass counts. I = m(2r) 2 = 4mr 2 m r m

4
Mass at a Radius Extended objects can be treated as a sum of small masses. A straight rod ( M ) is a set of identical masses m. The total moment of inertia is Each mass element contributes The sum becomes an integral axis length L distance r to r+ r

5
Rigid Body Rotation The moments of inertia for many shapes can found by integration. Ring or hollow cylinder: I = MR 2Ring or hollow cylinder: I = MR 2 Solid cylinder: I = (1/2) MR 2Solid cylinder: I = (1/2) MR 2 Hollow sphere: I = (2/3) MR 2Hollow sphere: I = (2/3) MR 2 Solid sphere: I = (2/5) MR 2Solid sphere: I = (2/5) MR 2

6
Point and Ring The point mass, ring and hollow cylinder all have the same moment of inertia. I = MR 2I = MR 2 All the mass is equally far away from the axis. The rod and rectangular plate also have the same moment of inertia. I = (1/3) MR 2 The distribution of mass from the axis is the same. R M M R axis length R M M

7
Playground Ride A child of 180 N sits at the edge of a merry-go-round with radius 2.0 m and mass 160 kg. What is the moment of inertia, including the child? Assume the merry-go-round is a disk. I d = (1/2)Mr 2 = 320 kg m 2 Treat the child as a point mass. W = mg, m = W/g = 18 kg. I c = mr 2 = 72 kg m 2 The total moment of inertia is the sum. I = I d + I c = 390 kg m 2 m M r

8
Parallel Axis Theorem Some objects don’t rotate about the axis at the center of mass. The moment of inertia depends on the distance between axes. The moment of inertia for a rod about its center of mass: axis M h = R/2

9
Perpendicular Axis Theorem For flat objects the rotational moment of inertia of the axes in the plane is related to the moment of inertia perpendicular to the plane. M I x = (1/12) Mb 2 I y = (1/12) Ma 2 a b I z = (1/12) M(a 2 + b 2 )

10
Spinning Coin What is the moment of inertia of a coin of mass M and radius R spinning on one edge? The moment of inertia of a spinning disk perpendicular to the plane is known. I d = (1/2) MR 2 The disk has two equal axes in the plane. The perpendicular axis theorem links these. I d = I e + I e = (1/2) MR 2 I e = (1/4) MR 2 M R M R next IdId IeIe

Similar presentations

OK

Rotational Dynamics Just as the description of rotary motion is analogous to translational motion, the causes of angular motion are analogous to the causes.

Rotational Dynamics Just as the description of rotary motion is analogous to translational motion, the causes of angular motion are analogous to the causes.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on inhabiting other planets that can support Ppt on vitamin b complex Ppt on gulliver's travels part 2 Ppt on indian textile industries in uganda Ppt on power system stability ball Ppt on management of water resources Ppt on year of faith Ppt on manas national park Ppt on bluetooth technology free download Ppt on internet services for class 7