Energy, Power & Work In Rotational Motion

Kinetic Energy in Rotational Motion (KE=½Iω2)

As we've seen before, in rotational problems, all the formulas are the same as for linear problems except the letters are different. Kinetic energy is no different, just swap rotational velocity (ω) for v and moment of inertia (I) for m and you're good to go.

Potential Energy In Rotational Motion

In linear motion, the main type of potential energy we saw was from gravity (mgh). While a rotating wheel doesn't really get mgh from spinning, that doesn't mean your professor can't find a way to use potential energy anyways, by hanging a mass off of a heavy wheel, or by having the wheel be lopsided, or with a rotational spring powering a catapult in a Pumpkin Chucking contest (½kx2), or a wheel rolling down a hill (next chapter).

Work In Rotational Motion (W=τΘ)

You may recall from earlier in physics that "work" in physics is when you introduce new energy into the problem from some source other than potential energy (mgh). Well, rotational problems are no different: If you want to get that jet engine spinning, an electric starter motor has to spin that up. If that kid wants a gyro toy to spin, she's got to pull that string (preferably with 25N of force for 1.2m).

Power In Rotational Motion (P=W/t or P=τΘ)

You won't see this too much on your homework or exams, but it may pop up as one of the sub-questions on a long problem, so it's worth revisiting power again. As with all things rotational, we'll have slightly different formulas than we did for linear power problems, but the overall effect is the same: how fast was energy put into the system?

Find Final Velocity of Falling Beam Using Energy

We return to the beam problem, but instead of looking at the instantaneous acceleration at the moment of release, we instead calculate final velocity after the beam has rotated downwards. If you aren't sure what potential energy and kinetic energy are, skip this video for now because there will be lots more rotational energy videos later in physics.