Rotational Inertia in two cylinders

In summary, when calculating the kinetic energies of two uniform solid cylinders with the same mass and angular velocity, but different radii, one must first convert the angular velocity from radians to revolutions per second. Then, using the moment of inertia formula, the kinetic energy can be calculated by plugging in the mass, radius, and converted angular velocity. It is important to pay attention to units and remember to multiply radians by 2pi before plugging in the numbers. If unsure, it is recommended to seek help from a teacher or expert.
  • #1
TheAce3317
5
0
Calculate the kinetic energies of two uniform solid cylinders, each rotating about its central axis. They have the same mass, 1.25 kg, and rotate with the same angular velocity, 235 rad/s, but the first has a radius of 0.18 m and the second a radius of 0.73 m.

I got 12112188.868 for ω, and 0.050625 for I


I have been using I=mr^2, and .5*Iω^2



I plugged everything in without changing any units, and got 1906125390.62499825 for the small one, which i know to be wrong. Then I thought I remembered something my teacher said about multiplying the radians by 2pi, and then I plugged all the numbers back in and got another large number.
 
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  • #2
nvm, ran out of time. getting help from my teacher tomorrow
 

FAQ: Rotational Inertia in two cylinders

1. What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It depends on the mass and distribution of an object's mass around its axis of rotation.

2. How is rotational inertia different from linear inertia?

Rotational inertia refers to an object's resistance to changes in its rotational motion, while linear inertia refers to an object's resistance to changes in its linear motion. In other words, rotational inertia is specific to an object's rotation around an axis, while linear inertia is specific to an object's movement in a straight line.

3. How does rotational inertia affect the movement of two cylinders?

The rotational inertia of two cylinders will depend on their individual masses and how their masses are distributed around their respective axes of rotation. If the cylinders have different masses or different distributions of mass, their rotational inertia will also be different. This can affect how they rotate and interact with each other.

4. How does the radius of a cylinder affect its rotational inertia?

The radius of a cylinder can affect its rotational inertia since it determines the distribution of its mass around its axis of rotation. A cylinder with a larger radius will have more mass distributed farther from its axis, resulting in a larger rotational inertia compared to a cylinder with a smaller radius.

5. Can rotational inertia be changed?

Yes, the rotational inertia of an object can be changed by altering its mass distribution or its axis of rotation. For example, if the mass of an object is moved closer to its axis of rotation, its rotational inertia will decrease. Additionally, changing the object's axis of rotation can also affect its rotational inertia.

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