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- DictionaryMo·ment of in·er·tia/ˌmōmənt əv əˈnərSHə/
noun
- 1. a quantity expressing a body's tendency to resist angular acceleration. It is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.
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Learn the definition, formula and examples of moment of inertia, a quantity that determines the torque needed for a desired angular acceleration of a rigid body. Find out how moment of inertia depends on the body's mass distribution, shape and axis of rotation.
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Aug 2, 2024 · Learn how to calculate the moment of inertia of a body, which is the opposition to changing its rotation speed about an axis. Find out the formula, the unit, and the examples of moment of inertia for different shapes and situations.
- The Editors of Encyclopaedia Britannica
Aug 2, 2023 · Moment of inertia is a physical quantity that resists a rigid body’s rotational motion. It depends on the shape, mass, and location of the axis of rotation. See how to calculate it for different objects and formulas.
- Moment of Inertia Example
- What Is Inertia?
- Moment of Inertia Definition
- Moment of Inertia of A System of Particles
- Moments of Inertia For Different Objects
- Parallel Axis Theorem
- Kinetic Energy in Rotational Motion
- Radius of Gyration
- Here Are A Few Solved Questions For You
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Imagine you are on a bus right now. You find a seat and sit down. The bus starts moving forward. After a few minutes, you arrive at a bus stop and the bus stops. What did you experience at this point? Yes. When the bus stopped, your upper body moved forward whereas your lower body did not move. Why is that? It is because of Inertia. Your lower body...
What is Inertia? It is the property of a body by virtue of which it resists change in its state of rest or motion. But what causes inertia in a body? Let’s find out. Inertia in a body is due to its mass. More the mass of a body more is the inertia. For instance, it is easier to throw a small stone farther than a heavier one. Because the heavier one...
So we have studied that inertia is basically mass. In rotational motion, a body rotates about a fixed axis. Each particle in the body moves in a circle with linear velocity, that is, each particle moves with an angular acceleration. Moment of inertia is the property of the body due to which it resists angular acceleration, which is the sum of the p...
For a system of point particles revolving about a fixed axis, the moment of inertia is: Moment of Inertia (I) = Σ miri2 where ri is the perpendicular distance from the axis to the ith particle which has mass mi. Example A system of point particles is shown in the following figure. Each particle has a mass of 0.3 kg and they all lie in the same plan...
For RodFor SphereFor HoopFor CylinderFor Rectangular objectsFor Ring/DiscThe Parallel Axis Theorem states, The moment of inertia of a body about an axis parallel to the body passing through its centre is equal to the sum of moment of inertia of the body about the axis passing through the centre and product of the mass of the body times the square of the distance between the two axes. Its formula is, I = Ic + Mh2 where, ...
What is the analogue of mass in rotational motion? To answer this question, we have to derive the equation of kinetic energy in rotational motion. Consider a particle of mass m at a distance from the axis with linear velocity =vi = riω. Therefore, the kinetic energy of this particle is, ki = 1/2 mivi2 = 1/2 mi(ri )2ω2 where mi is the mass of the pa...
As a measure of the way in which the mass of a rotating rigid body is distributed with respect to the axis of rotation, we define a new parameter known as the radius of gyration. It is related to the moment of inertia and the total mass of the body. Notice that we can write I = Mk2 where khas the dimension of length. Therefore, the radius of gyrati...
Question 1.The moment of inertia depends on: a) mass of the body b) shape and size of the body c) distribution of mass about the axis of rotation d) all of the above Answer: d) all of the above. All the factors together determine the moment of inertia of a body. Question 2:Find the moment of inertia of a disc of mass 5 kg and radius 30 cm about the...
Learn what is moment of inertia, the property of a body that resists angular acceleration, and how to calculate it using a formula. Explore the concept with examples, theorems, and diagrams of different objects.
Learn the concept of moment of inertia, a quantity that measures the resistance of a body to angular acceleration. Find out the formulas, factors, and examples of moment of inertia for different objects and shapes.
- 66 min
- The moment of inertia of a rigid body depends only on the distribution of mass of the body about the axis of rotation and is independent of the spe...
- The moment of inertia of a hollow cylinder will be larger than the moment of inertia of the disc because most of its mass is located away from the...
- The moment of inertia is a scalar quantity.
- I = (⅖)MR 2
Learn how to calculate the moment of inertia of different shapes and objects with respect to a specific axis. The moment of inertia measures the resistance of a body to change its rotational motion and is related to the angular momentum.
Learn the definition and formula of moment of inertia, a rotational analogue of mass in linear motion. Find out how it depends on the distribution of mass and the axis of rotation.
