ROTATION AND INERTIA
Chapter 8 Section 2
Center of Mass


Center of Mass – The point at which all the mass of
the body can be considered to the concentrated
when analyzing translational motion.
The special point around which the object rotates
neglecting all other forces, except gravity.
Rotational and Translational Motion


The complete motion of an object can be described
in translational (linear) motion and rotational
motion.
Example:
 Throwing
 As
a hammer into the air.
the hammer rotates around its center of mass, the
hammer travels as a point mass in its parabolic path just as
predicted in projectile motion.
Parabolic Path of a Projectile

The center of masses of the ball and the rotating
bat both follow their parabolic path.
Center of Gravity

The center of gravity and the center of mass can be
considered the same thing at the basic physics level.
Stability

The block topples when the center of gravity
extends beyond its support base.
Moment of Inertia



Moment of Inertia – The measure of the resistance
of an object to changes in rotational motion.
Moment of Inertia depends on both the object’s
mass and the distribution of the mass around the
axis.
Mass located farther away from the axis has a
greater moment of Inertia.
Newton’s Second Law

Translational Motion
 When
a net force acts on an object, the resulting
acceleration of the object depends on the objects mass.

Rotational Motion
 When
a net torque acts on an object, the resulting
change in the rotational motion of the object depends
on the object’s moment of Inertia.
The Moment of Inertia for a Few
Shapes
The Moment of Inertia for a Few
Shapes Cont.
Moment of Inertia



Variable for Moment of Inertia = I
Units for Moment of Inertia = kgm2
Make sure that all units are in SI units when
calculating the moment of inertia.
Equilibrium

Equilibrium requires both a net force of zero and a
net torque of zero
= 0 Nm
 ΣF = 0 N
 ΣΤ


Translational Equilibrium is when the net force is
equal to zero.
Rotational Equilibrium is when the net torque is
equal to zero.
Example Problem #1

What is the moment of Inertia of a stick around its
center of mass if the stick has a mass of 345 grams
and a length of 2 feet?
Example Problem #1

I = 1.07x10-2 kgm2
Example Problem #2

An 8.5 m long ladder weighs 350 N. The ladder
leans against a frictionless vertical wall. If the
ladder makes an angle of 60 degrees with the
ground, find the force exerted on the latter by the
wall and the force exerted on the latter by the
ground.
Example Problem #2 Answer

Fx = Rx – Fwall = 0
Fy = Ry – Weight = 0
T = -(L/2)(Weight)(Sin30)+(L)(Fwall)(Sin60) = 0

Fwall = 101.04N



Rx = 101.04N
Ry = 350N

Fground = 364.30N @ 73.90°
