Moment of inertia and rotational kinetic energy

Click For Summary
SUMMARY

The discussion focuses on the concept of moment of inertia and its relationship to rotational kinetic energy. Moment of inertia (I) is defined as I = ∫ dm r², which relates torque (τ) to angular acceleration (α) through the equation τ = Iα, analogous to Newton's second law (F = ma). The kinetic energy associated with rotation is expressed as KE = 1/2 Iω², paralleling the linear kinetic energy formula. Understanding these relationships is crucial for analyzing rotational dynamics in physics.

PREREQUISITES
  • Understanding of basic physics concepts such as torque and angular acceleration.
  • Familiarity with Newton's laws of motion, particularly F = ma.
  • Knowledge of calculus, specifically integration for deriving moment of inertia.
  • Basic understanding of rotational motion and kinetic energy equations.
NEXT STEPS
  • Study the derivation of moment of inertia for various geometries and shapes.
  • Explore the application of rotational dynamics in real-world scenarios, such as in machinery.
  • Learn about the conservation of angular momentum and its implications in rotational systems.
  • Investigate advanced topics in rotational kinetic energy, including energy transfer in rotating systems.
USEFUL FOR

Students of physics, mechanical engineers, and anyone interested in understanding the principles of rotational motion and energy in physical systems.

CrazyNeutrino
Messages
99
Reaction score
0
I can't seem to understand moment of inertia. What does it mean and how is it derived ?
How does it relate to rotational kinetic energy.
 
Physics news on Phys.org
Hi CrazyNeutrino! :smile:

From the PF Library on moment of inertia …

Moment of Inertia … relates rotational force (torque) to rotational acceleration in the same way that mass relates ordinary (linear) force to ordinary acceleration.​

ie τ = Iα just like F = ma

(and KE = 1/2 Iω2 just like 1/2 mv2)

it is derived from I = ∫ dm r2
 
Why dm r^2?
 
CrazyNeutrino said:
Why dm r^2?

because for a point mass m at distance r from the axis, subjected to a force F,

the torque is τ = Fr, and the angular acceleration is α = a/r

τ = Iα means Fr = Ia/r

but F = ma (good ol' Newton's second law)

so mar = Ia/r

so I = mr2​

(and moment of inertia of the whole = sum of moments of inertia of the parts, giving us ∫ dm r2)
 

Similar threads

High School The physics of flywheel launchers (like tennis ball shooters)
  • · Replies 60 ·
3
Replies
60
Views
6K
Graduate Lagrangian mechanics - rotating rod
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Resolve moment of inertia at an angle
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Hamilton’s principle maximises potential energy?
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Moment of Inertia about an axis and Torque about a point
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad The proportion of kinetic energy of a rotating rigid body?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Effects of External Torques on the Angular Momentum of Asymmetric Bodies
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How to find moment of inertia of an insect?
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Torque and Rotational Kinetic Energy Relationship
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why Do Different Objects Share Similar Moments of Inertia?
  • · Replies 1 ·
Replies
1
Views
2K