a grade-school project, students construct a mobile representing
some of the major food groups. Their completed artwork is shown below.
Find the masses , ,
are required for a perfectly balanced mobile.
The Dynamics of Rotation
with the moment of inertia
the general definition of the moment of inertia to find the moment
of inertia for the dumbbell shaped object shown below. Note the axis
of rotation goes through the center of the object and points
out of the page. In addition, assume that the masses may be treated
as point masses.
We see that and .
Then the moment of inertia
motor in an electric saw brings the circular blade from rest
up to the rated angular velocity of 80.0 rev/s in 240.0 rev.
One type of blade has a moment of inertia of .
What net torque (assumed constant) must the motor apply to the
We need to find the angular acceleration so that we can use which
is called Newton's Second Law for rotational motion. The equation
to use to find the angular acceleration is .
Solving for :
putting this expression into the torque equation and substituting:
to the Dynamics of Rotation 2