A solid disk of radius 23.4cm and mass 1.45kg....

In summary, a solid disk and a solid cylinder with different radii and masses are initially spinning at different rates. After the cylinder is dropped onto the disk, friction causes both objects to rotate in the same direction at a common angular velocity of 26.7 rad/s. To determine the change in mechanical energy, we can use the equation K=Iwf^2-Iwi^2 where K is the kinetic energy, I is the moment of inertia, wf is the final angular velocity, and wi is the initial angular velocity. However, more information is needed to calculate the moment of inertia for the combined system.
  • #1
HappyFlower
30
1

Homework Statement


A solid disk of radius 23.4 cm and mass 1.45 kg is spinning at 43.1 radians per second. A solid cylinder of radius 12.1 cm and mass 3.33 kg is not spinning. The cylinder is dropped into the center of the spinning disk. After a short time friction has caused both objects to engage and turn in the same direction and rate.
a) Determine final rotational direction and angular velocity of the system?
b) Determine the change in mechanical energy of the system?

Homework Equations

The Attempt at a Solution


i found a) 26.7 rad/s
I am having trouble finding the mechanical energy I don't know which equation I should use. I tried using
K=Iwf^2-Iwi^2
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  • #2
Please show your work.
 
  • #3
Orodruin said:
Please show your work.
I fixed it.
 
  • #4
HappyFlower said:
I fixed it.
Rather than just writing down equations, you should explain what those equations are for. For instance:

You have a cylinder sitting on a disk such that both are rotating at the same angular velocity. You have determined that angular velocity. What is the total rotational kinetic energy of the assembly?
 

What is the formula for calculating the moment of inertia of a solid disk?

The moment of inertia of a solid disk can be calculated using the formula I = (1/2)mr^2, where m is the mass of the disk and r is the radius.

How do you find the moment of inertia of a solid disk with a known mass and radius?

To find the moment of inertia of a solid disk with a known mass and radius, simply plug in the values into the formula I = (1/2)mr^2.

What is the unit of measurement for moment of inertia?

The unit of measurement for moment of inertia is kilogram-meter squared (kgm^2).

How does the moment of inertia of a solid disk change if the radius is doubled?

If the radius of a solid disk is doubled, the moment of inertia will increase by a factor of four. This is because the moment of inertia is directly proportional to the square of the radius.

Can the moment of inertia of a solid disk be negative?

No, the moment of inertia of a solid disk cannot be negative. It is always a positive value as it represents the resistance of an object to changes in rotational motion.

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