A uniform disk of radius 0.48 m is mounted
on a frictionless, horizontal axis. A light cord wrapped around the disk supports a 1.4 kg object, as shown. When released from rest the object falls with a downward acceleration of 3.6 m/s^2.
What is the moment of inertia of the disk?
To find the moment of inertia of the disk, we can use the formula:
I = (m * g * r) / a
Where:
I is the moment of inertia,
m is the mass of the object (1.4 kg),
g is the acceleration due to gravity (9.8 m/s^2),
r is the radius of the disk (0.48 m),
a is the downward acceleration of the object (3.6 m/s^2).
Plugging in the values:
I = (1.4 kg * 9.8 m/s^2 * 0.48 m) / 3.6 m/s^2
Now we can solve this equation to find the moment of inertia.