1. The angular velocity of the disk is
omega(disk) = 0.0462 rad/sec
2. The angular momemtum of the disk (which has mass M = 5321 kg) is
L(disk) = 768 kg*m^2/s
3. Joe's angular momentum around the center of the disk must be
equal and opposite:
L(disk) + L(Joe) = 0
L(Joe) = -L(disk) = -768 kg*m^2/s
4. Joe's mass is 60 kg, and his distance from the center of the
disk is R = 2.5 meters. We can compute his moment of inertia
around the center of the disk:
I(Joe) = m(Joe)*R*R
= 1500 kg*m^2
We can now compute Joe's angular velocity:
L(Joe) = I(Joe) * omega(Joe)
L(Joe) -768 kg*m^2/s
--> omega(Joe) = ---------- = ------------------
I(Joe) 1500 kg*m^2
omega(Joe) = 0.511 rad/s
5. How fast is Joe moving? His angular velocity relative to
that of the disk is
omega_diff = omega(Joe) - omega(disk)
= -0.556 rad/sec
so the magnitude of the linear speed of his feet, relative to
the disk, is
speed = abs(omega_diff*R) = 1.39 m/s