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### Course: Physics archive>Unit 7

Lesson 2: Torque, moments, and angular momentum

# Rotational kinetic energy

David explains what rotational kinetic energy is and how to calculate it. Created by David SantoPietro.

## Want to join the conversation?

• How come the units aren't equal on both sides of the formula?
If you write out the units of K = 1/2 I 𝝎^2 in SI-units you get:
kg m^2 s^-2 = kg m^2 rad^2 s^-2
This would mean the rad unit just appears and dissapears. Is this correct? How can this be explained?
• Since no one solved your question...

Radians can disappear or reappear in an equation because the unit itself is a ratio (if I remember correctly it should be the ratio of the radius to the arc length where it is the same length as the radius [1 rad is like the 2π in 2πr=C where this time it's just 1r=part of C])].

Due to it being an equal (1:1) ratio, it effectively cancels itself out if you want it to. You can google dimensionless units for more information.

• David says that the moment of inertia is mr^2, but isn't the moment of inertia of a sphere 2/5mr^2? Does the summation result in that quantity? Or is 2/5mr^2 only used in special circumstances?
• the moment of inertia of a single point mass a distance r from the turning point is I = mr^2

for all other shapes is more complicated; the half circle is just one example
• In the baseball problem shown in this video, why did the relationship v=ωr fail?
v=40m/s but ωr=50*0.07 m/s=3.5 m/s ! Did I make any mistake here?
• In the formula v=wr, v is the tangential speed of a particular point on the baseball.
What you have calculated using the formula is the tangential speed of a point on the outermost edge of the ball for which the w is 50s^(-2) and r=0.07m.
What v=40m/s here in the question given is the translational velocity of the center of mass of the baseball
• At , why we got different masses for different points? Aren't they the same? because they are all on the same ball.
• With calculus, to get the real rotational kinectic energy, you would use all points of the baseball, each with the same infinitely small mass (considering the density is constant for the ball).
• If the total kinetic energy is the sum of both kinds of energies, does that mean that the energy I've used to throw the ball is going to be divided between translational and rotational kinetic energy? In an ideal world, if I could minimize the rotation when throwing, would the ball go faster/land further away from me?
• If you could minimize rotation without otherwise reducing the energy you put into the throw, then sure, you would be able to throw the ball harder.
Whether it would go further is a different questions. The spin of a ball causes interesting effects with air resistance and in some cases can cause a spinning ball to pass more easily through the air than a non spinning ball. Golf balls have dimples to maximize the effect of spin on the distance of the golf shot.
• How could be the angular velocities the same for every point ?
• I think we need to review the basic concepts of rotation here. Each point on a rotating rigid object possesses the same angular velocity but different linear velocities. If the angular velocities weren't the same at every point, the object would break apart.
• How would you find the moment of inertia of a sphere using calculus? Would you use integration or derivation? And how?
• You would use integration because you are adding up a bunch of little inertias to get the total moment of inertia.
• doesn't the ball rotate backwards?
• By "backwards" he means spinning counterclockwise relative to the perspective shown. It is possible that the ball was thrown in such a way that it rotated this way, but only the magnitude of velocity, angular or otherwise, matters when determining KE. The direction of rotation is not relevant.