# Day 51: Rotational Kinetic Energy

*AP Physics C: *Today we derived the formula for rotational kinetic energy and showed that the total kinetic energy is simply the sum of the transnational and rotational energies. We teased out the relationships by analyzing the following 3 problems.

#1 Because we haven’t seen the rotational kinetic energy formula yet, they had to determine the linear speed of each sphere first for this problem:

#2. This one is easy.

#3. For this one, they had to figure out the *net* velocity of each sphere. The orange ones were easy. The blue ones were trickier (2D vectors!).

And low and behold … all that crazy work to work out #3 turned out to yield the sum of #1 and #2!

*NGSS Science and Engineering Practices
#5. Using mathematics and computational thinking*