6.3 Rotational Dynamics

​6.3 Rotational Dynamics

By NABILAH Moe

6.3 Rotational Dynamics

By end of this lesson, students should be able to:

• Define the moment of inertia.

• State net torque.

If you want to rotate something that is at rest initially, is it easy or a bit difficult?

Why?

Law of inertia

Tendency of an object to resist any change in its state of rest or motion at a constant velocity. Any object that has mass has this tendency!

So, for a rotating body which consists of mass in motion, there is resistance to changes from rest or from rotation motion. This resistance to changes is called moment of inertia, I.

What factors affect the resistance to changes of a rotating body (moment of inertia)?

Moment of Inertia, I

Since a body is made up of many particles, with masses m₁, m₂, … at distance r₁, r₂, … from the axis of rotation, moment of inertia can be defined as the sum of products of the mass of each particle and the square of its respective distance from the rotation axis.

​Large I requires more torque to change the body’s  because it is harder to rotate!

​Moment of inertia I for various rigid body of mass M about axes through the centre of mass

Before this, you have learned that when a body’s rotational motion is in equilibrium, the body will either be stationary, or rotating at a constant angular velocity (no acceleration). So, the net torque will be zero.

But now, what if a rotating body is NOT in equilibrium?

Net torque

A rigid body that experiences a net torque about rotation axis, undergoes an angular acceleration!

The net torque acting on a rigid body is the cause of the body’s angular acceleration.

Multiple Choice

What does the moment of inertia of a rigid body depend on?

• Only the mass of the body

• Only the shape of the body

• Mass, shape, and axis of rotation

• Only the angular velocity of the body
  

Multiple Choice

Which of the following shapes has the largest moment of inertia, assuming equal mass and radius?

• Solid sphere

• Solid cylinder

• Hoop or ring

• Thin rod through center

Multiple Choice

What is the SI unit of moment of inertia?

• N m

• kg m²

• rad/s²

• J s

Multiple Choice

If a net torque is applied to a rigid body, what happens?

• The body moves linearly

• The body’s angular velocity remains constant

• The body undergoes angular acceleration

• The moment of inertia changes

Multiple Choice

A solid disk and a hoop both have the same mass and radius. Which one is easier to rotate?

• The hoop

• The disk

• Both are equally easy

• Depends on the torque applied

Multiple Choice

What happens to angular acceleration if the moment of inertia increases while torque remains constant?

• It increases

• It decreases

• It remains unchanged

• It becomes zero
  

Summary...

Each airlines share ONE thing you have learned today. Cannot be the same thing!