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Newton's first law

Every body (that has mass) in a state of rest tends to remain at rest. Similarly, every body (that has mass) in a state of motion tends to remain inmotion in a straight line. In both cases, the body tends to remain in its current state unless compelled to change its state by external forces actingupon it.

This law is sometimes referred to as the "Law of Inertia" -- objects that have mass don't like to change their velocity.

Newton's second law

Newton's second implies (once again paraphrasing) that the tendency to remain in the state of rest or motion depends on the amount of mass possessed by thebody.

The greater the mass, the greater must be the external force required to cause the body to change its state by a given amount. You will recognize this asbeing characterized by the equation that tells us that acceleration (change of velocity) is proportional to the applied force and inversely proportional to theamount of mass.

Rotating rigid bodies

Similar considerations also apply to the rotation of rigid bodies. In the case of rigid-body rotation, however, it isn't simply the amount of mass that isimportant. The geometrical distribution of that mass also has an impact on the reluctance of a rotating body to change its state. We refer to this as rotational inertia , which is sometimes called the moment of inertia .

Rotational inertia or moment of inertia?

Rotational inertia and moment of inertia are simply two names that mean the same thing (some authors prefer one, otherauthors prefer the other)

I don't have a preference for either, but for consistency with the textbook currently being used for introductory physics courses at the college where Iteach, I will use the term rotational inertia instead of moment of inertia .

An example

For example, the same amount of mass can be used to create

  • a tall solid cylinder with a small radius or
  • a thin disk with a large radius or
  • a very thin disk with most of the mass concentrated around the outer circumference of the disk.

When rotated about its central axis, either disk has a greater rotational inertia than thecylinder, and the disk with most of its mass concentrated around the outer circumference has a greater rotational inertia than the other two.

The rotational inertia increases as the mass is moved further from the axis of rotation, and the effect is proportional to square of that distance.As a result, given that the total mass is the same in all three cases, a greater external force is required to cause either disk to changeits rotational state than is required to cause the cylinder to change its rotational state.

Work and kinetic energy

You also learned in an earlier module that work must be done on an object tocause it to have kinetic energy, and the kinetic energy possessed by an object is proportional to one-half of the product of the object's mass and the squareof its velocity.

KE = (1/2)*m*v^2

where

  • KE represents translational kinetic energy
  • m represents mass
  • v represents velocity

The rotational kinetic energy of a rotating body

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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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