1. Rotational Equilibrium and Dynamics
Rotation and Inertia

2. Center of Mass
There is a point about which an object will rotate if the only force acting on the object is gravity
Center of mass – the point at which all the mass of the body can be considered to be when analyzing translational motion
Translational motion is any motion that’s not rotational

3. Center of Mass
Center of gravity – the position at which the gravitational force acts on the extended object as if it were a point mass
We will treat center of mass and center of gravity as the same point

4. Moment of Inertia
Some objects have several axes around which they can rotate.
Some axes are easier to rotate around than others
This is because of the object’s moment of inertia
Moment of inertia – the tendency of a body rotating about a fixed axis to resist a change in rotational motion

5. Moment of Inertia Moment of inertia is rotational analog of mass
Anytime we would use mass for a rotating object, we use moment of inertia
The main difference is that mass remains constant for an object, assuming the object doesn’t change
Moment of inertia changes depending on which axis the object is rotating around

6. Moment of Inertia
The farther an object’s mass is from the axis of rotation, the larger the object’s moment of inertia
The larger the object’s moment of inertia, the harder it is to rotate
Therefore, solid objects have smaller moments of inertia than hollow objects with the same mass and radius
Solid objects rotate faster than hollow ones

7. Moment of Inertia
When a net torque acts on an object, the resulting change in rotational motion of the object depends on the object’s moment of inertia
Moment of inertia is measured in kilogram meters2 (kgm2)
Calculating moment of inertia depends of the object’s shape and the axis of rotation
It will involve multiplying the object’s mass times its radius squared for circles and spheres (MR2) or length squared for cylinders (Ml 2)
This is then multiplied by a fraction (½, 2/5, etc.)

8. Moment of Inertia

9. Rotational Equilibrium
For an object to be in equilibrium, the object must experience zero net force and zero net torque
Zero net force gives the object translational equilibrium
Called the first condition of equilibrium
Just add all of the forces up

10. Rotational Equilibrium
Zero net torque gives the object rotational equilibrium
Called the second condition of equilibrium
Pick an axis of rotation and add all of the torques
A force that acts along the axis of rotation will not produce a torque
So you should try to position unknown forces along the axis of rotation

11. Rotational Equilibrium