# Inertia in Rotation: Rotational vs Other Motion

• jmf322
In summary: Or let's say the masses of the objects that are rotating are exactly the same. but one mass is further away from the axis of rotation than the other..., which is more difficult to change the rotation of, and how much more difficult?
jmf322
what is the difference between inertia in rotational motion vs. inertia in other motion

They're just two different physical quantities, both of which happen to be conserved. Conservation of linear momentum is a result of the translational symmetry of the laws of physics (ie, the laws are the same here as they are there), while conservation of angular momentum is a result of the rotational symmetry (the laws are the same when your axes are aligned this way as when they are aligned that way).

The inertia of a particle (inertia = mass) is its resistance to a change in its velocity. This could be a change in direction or speed or both. This is what is meant by the equation a = F/m, or F = ma. For a given applied force, the particle's rate of change of velocity is inversely proportional to its mass (inertia).

The case for rotation is similar. The rotational inertia of a body measures its resistance to a change in the angular velocity of the body. The rotational inertia depends not only on the mass, but how that mass is distributed about the axis of rotation. It has units of mass x distance^2. The rotational inertia determines how the angular velocity will change as a result of a given applied torque. The more spread out the mass is in relation to the axis of rotation, the more the body resists a change in angular velocity.

which are the factors that affect rotational inertia and how are mathematically connected?

let's say specificaly for disks (with ignorable height) that an axis in their center rotates them

mather said:
which are the factors that affect rotational inertia and how are mathematically connected?

let's say specificaly for disks (with ignorable height) that an axis in their center rotates them

What is more difficult to change the rotation of, a lot of mass rotating about an axis it is far away from, or a little bit of mass rotating close to an axis of rotation?

pgardn said:
What is more difficult to change the rotation of, a lot of mass rotating about an axis it is far away from, or a little bit of mass rotating close to an axis of rotation?

let's say that the diameter of the disks is the same

ofcourse the heavier disk will be more difficult to rotate

but how much more difficult?

mather said:
let's say that the diameter of the disks is the same

ofcourse the heavier disk will be more difficult to rotate

but how much more difficult?

Or let's say the masses of the objects that are rotating are exactly the same. but one mass is further away from the axis of rotation than the other..., which is more difficult to change the rotation of, and how much more difficult?

## 1. What is inertia in rotational motion?

Inertia in rotational motion refers to an object's resistance to changes in its rotational state. It is similar to inertia in linear or translational motion, which is an object's resistance to changes in its linear motion.

## 2. How does rotational inertia differ from linear inertia?

Rotational inertia differs from linear inertia in that it specifically applies to an object's rotational motion, while linear inertia applies to an object's linear motion. Rotational inertia also depends on the distribution of mass in an object, while linear inertia does not.

## 3. What factors affect rotational inertia?

The main factor that affects rotational inertia is the distribution of mass in an object. Objects with more mass concentrated farther away from the axis of rotation have a higher rotational inertia. The shape and size of an object also play a role in determining its rotational inertia.

## 4. How does rotational inertia affect an object's motion?

Rotational inertia affects an object's motion by determining how easily it can be rotated or stopped from rotating. Objects with a higher rotational inertia require more torque to rotate or stop, while objects with a lower rotational inertia require less torque.

## 5. Can objects with different shapes have the same rotational inertia?

Yes, objects with different shapes can have the same rotational inertia if they have the same mass and their mass is distributed in the same way. This is known as the parallel axis theorem, which states that the rotational inertia of an object can be calculated by adding the rotational inertia of its individual parts.

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