Rotational Inertia
 net  I
Newton’s Second Law
for Rotation
Rotational Inertia (Moment of Inertia) (I) – The slope of a graph of torque vs.
angular acceleration.
– The tendency of an object to
continue in its same state of
rotation.
– A measure of an object’s
resistance to changes in its
rotation.
– How difficult it is to start or stop
the rotation of an object.
Rotational Inertia
Consider the blue and red Inertia Wands.
They have the same mass.
Shake them up and down to confirm.
Now twist them side to side.
The blue Inertia Wand is much harder to twist!
Why!
Rotational Inertia of Point Masses Lab
The rotational inertia depends on the mass and on where that mass is!
Notice that the units of the rotational inertia (kgm2) also
indicate that it depends on the mass and the distance the
mass is from the axis of rotation.
Purpose: To create graphical and mathematical representations of the
relationship between the rotational inertia (I), the total mass (m),
and the distance the masses are from the axis of rotation (r) for a
system of particles consisting of two point masses.
Rotational Inertia of Point Masses Lab
  rF sin 
  rFT
r  radius of the pulley
F  FT in the string
  90
r
The clamp-on Super Pulley must be
adjusted at an angle, so that the thread
runs in a line tangent to the point where it
leaves the 3-step Pulley and straight down
the middle of the groove on the clamp-on
Super Pulley (Figure 1.2).
Rotational Inertia of Point Masses Lab
  rF sin 
  rFT
r  radius of the pulley
F  FT in the string
Fg  FT

FT


F

m
a
 y
y
  90

To find a
Since the string doesn’t slip, the
linear acceleration of the masses is
equal to the tangential acceleration
of the outside of the pulley.
aof the masses  at of the pulley
at   r
Since the masses
are accelerating
downward.

Fg
FT  Fg  ma
FT  Fg  ma
FT  mg  ma
FT  m g  a 
Rotational Inertia of Point Masses Lab
  rFT
FT  m g  a 
at   r
  rm g   r 
Newton’s Second Law
  I

I

I
rm g   r 

Experimental
Rotational Inertia