A 4.0 kg pulley of radius 0.15 m is pivoted about an axis through its center. What constant torque is required for the pulley to reach an angular speed of 25 rad/s after rotating 6.0 revolutions, starting from rest?
What moment of inertia do I use to figure our the torque?
I would model the pulley as a flat disk.
http://hyperphysics.phy-astr.gsu.edu/hbase/tdisc.html
1/2 m r^2
To figure out the moment of inertia to calculate the torque required for the pulley, you need to consider the pulley's shape and the axis of rotation.
In this scenario, the pulley is a solid disk, rotating about an axis through its center. The moment of inertia for a solid disk rotating about its central axis is given by the formula:
I = 1/2 * M * R^2
Where:
I is the moment of inertia
M is the mass of the pulley
R is the radius of the pulley
In this case, the mass of the pulley (M) is given as 4.0 kg, and the radius (R) is given as 0.15 m.
Substituting these values into the formula, we get:
I = 1/2 * 4.0 kg * (0.15 m)^2
= 0.45 kg*m^2
So, the moment of inertia (I) for this pulley is 0.45 kg*m^2.
Now that you have the moment of inertia, you can proceed to calculate the torque required.