Download the App!

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

(1I) Four identical particles of mass $m$ are mounted at equal intervals on a thin rod of length $\ell$ and mass $M,$ with one mass at each end of the rod. If the system is rotated with angular velocity $\omega$ about an axis perpendicular to the rod through one of the cnd masses, determine $(a)$ the kinetic energy and $(b)$ the angular momentum of the system.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a) $\left(\frac{7}{9} m+\frac{1}{6} M\right) \ell^{2} \omega^{2}$b) $\left(\frac{14}{9} m+\frac{1}{3} M\right) \ell^{2} \omega$

Physics 101 Mechanics

Chapter 11

Angular Momentum; General Rotation

Moment, Impulse, and Collisions

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Cornell University

University of Michigan - Ann Arbor

Hope College

McMaster University

Lectures

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

04:16

Two particles of masses $m…

01:43

A rod of mass $2 \mathrm{~…

02:09

(II) A uniform horizontal …

05:39

Three small particles are …

05:31

Rigid rods of negligible m…

02:49

Two Particles In Fig. $11-…

03:28

02:08

02:05

Two particles, each with m…

06:31

01:45

Two particles of mass $m_{…

01:04

A rod of length $L$ connoc…

03:17

Gig. 10-37, two particles,…

occasional inertia of the compound object is the sum of the individual moments of inertia. So the total moment of inertia I would be equaling to the moment of inertia of the particles, plus the moment of inertia of the Rod. And so this would be mass times zero squared plus mass times I'll over three squared plus mass times to L over three squared plus M l squared plus 1/3 m l squared. And so this is gonna be equal to l squared, multiplied by 14 over nine times M plus 1/3 times the mass of the rod. And so for party, the kinetic energy the rotational kinetic energy would be 1/2 times the moment of inertia times the angler velocity squared. This is equal in 1/2 times 14 over nine times M plus 1/3 and times l squared Omega squared And this is gonna be equaling seven over nine and plus one over six. Um multiplied by again l squared Omega squared. This would be your answer for part A for part B, then the angular momentum would be equal in the moment of inertia times omega. And this would simply be 14 over nine times and the mass of a particle plus 1/3 times the mass of the rod multiplied by El Square times Omega, The angular velocity. This would be your answer for Part B and her answer for part A. That is the end of the solution. Thank you for

View More Answers From This Book

Find Another Textbook

01:31

what makes planet Earth different from the other planet in the solar system?…

01:28

Which of the following are correct about components of Skills Related Fitnes…

02:11

Why is it better to use the pedestrian lane when crossing the street than cr…

01:20

which law states that forces act equal magnitude and in opposite direction

01:52

energy called Motion energy and can be computed using the formula___

02:26

if you have two bag of rice;bag A is 5 kilograms and bag B is 10 kilograms. …

03:30

which has more mass, a kilogram of cotton or a kilogram of iron?A the ironB …