IB Physics Topic A.4.2 Moment of Inertia Revision Notes (HL)

IB Physics Topic A.4.2 Moment of Inertia Revision Notes (HL) | RevisionDojo

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Definition of Moment of Inertia

Definition

Inertia

Inertia is the tendency of an object to resist changes in its state of motion.

In other words, it quantifies how difficult it is to change the rotational motion of an object.
It depends on two factors:
1. Mass of the object
2. Distribution of mass relative to the axis of rotation
Mathematically, the moment of inertia for a system of point masses is given by: $$I = \sum m_i r_i^2$$ where:
1. $m_i$ is the mass of each point
2. $r_i$ is the distance of the mass from the axis of rotation

Example

Single particle: A particle of mass $m$ at a distance $R$ from the axis has a moment of inertia $I = mR^2$.
Multiple particles: Two particles, each of mass $m$, at distances $R_1$ and $R_2$ from the axis have a total moment of inertia $I = mR_1^2 + mR_2^2$.

Moment of Inertia as the Rotational Equivalent of Mass

In linear motion, mass measures an object's resistance to changes in velocity.
Similarly, in rotational motion, the moment of inertia measures an object's resistance to changes in angular velocity.

Note

The moment of inertia depends on the axis of rotation.
The same object can have different moments of inertia if rotated about different axes.

Rotational Kinetic Energy

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Definition of Moment of Inertia

Definition

Inertia

Inertia is the tendency of an object to resist changes in its state of motion.

In other words, it quantifies how difficult it is to change the rotational motion of an object.
It depends on two factors:
1. Mass of the object
2. Distribution of mass relative to the axis of rotation
Mathematically, the moment of inertia for a system of point masses is given by: $$I = \sum m_i r_i^2$$ where:
1. $m_i$ is the mass of each point
2. $r_i$ is the distance of the mass from the axis of rotation

Example

Single particle: A particle of mass $m$ at a distance $R$ from the axis has a moment of inertia $I = mR^2$.
Multiple particles: Two particles, each of mass $m$, at distances $R_1$ and $R_2$ from the axis have a total moment of inertia $I = mR_1^2 + mR_2^2$.

Moment of Inertia as the Rotational Equivalent of Mass

In linear motion, mass measures an object's resistance to changes in velocity.
Similarly, in rotational motion, the moment of inertia measures an object's resistance to changes in angular velocity.

Note

The moment of inertia depends on the axis of rotation.
The same object can have different moments of inertia if rotated about different axes.

Rotational Kinetic Energy

Definition

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Note

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Excepteur sint occaecat cupidatat non proident

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Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics A.4.2 Moment of Inertia Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

Definition of Moment of Inertia

Moment of Inertia as the Rotational Equivalent of Mass

Rotational Kinetic Energy

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

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Definition of Moment of Inertia

Moment of Inertia as the Rotational Equivalent of Mass

Rotational Kinetic Energy

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account