- #1

- 105

- 3

^{2}I dont understand why. Here is my reasoning

Consider this shape (the ball is a point), the moment of inertia is MR

^{2}, there I agree

but now

what happens when you add another point on the other side

since I = ΣMR

^{2}then this is 2MR

^{2}

What about a ring or circle, that is nothing more than a bunch of points all the same distance from the center

so how many points are there? The circumference

so I= πR

^{2}MR

^{2}

I know that different objects moment of inertia differ by a number in front, like 1/2 or 3/5

Why is their no number prefix for Inertia in front of the formula for a hoop/ hollow cylinder/ circle that represents its circumference? How is this even derived?

Second question, How do you represent the angular Kinetic energy of this object?

Left Point = A

Right point = B

½ I ω

_{A}

^{2}+ ⅓ I ω

_{B}

^{2}

½ I ( ω

_{A}

^{2}+ω

_{B}

^{2})

both objects have same ω so

½ I 2ω

^{2}

Or

do I use ω to represent the angular velocity of the whole object and just keep it as

½ I ω

^{2}with whatever I is from the previous question?