Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.60 m. The merry‑go‑round is spinning at 24.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. What is the equation of the total moment of inertia? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses.

To calculate the temperature of the log we need the Stefan-Boltzmann's law:

P=A*ε*σ*T⁴, where P is the power emitted by the body,
A is the total surface area of the body, in our case it is a cylinder so A=r²π*h where r is the radius of the base of the cylinder and h is the height of the cylinder, 
σ is the Stefan-Boltzmann constant, T is temperature and ε is emissivity .
Here we are approximating the log to be a black body. 

The area of the cylinder:

A=r²*π*h, r=d/2=0.75/2=0.375 m, where d is the diameter, h=0.18 m

A=0.07948 m²

Lets solve the equation for temperature T:

T⁴=P/(σ*ε*A) and take the 4th root to get T:

T=⁴√{P/(σ*ε*A)}=⁴√{38000/((5.67*10^-8)*1*0.07948)} = ⁴√(8.432*10^12)= 1704.06 C

So the temperature of the log is T= 1704 C