Calculating Angular Velocity and Energy Loss in a System of Two Rotating Discs

In summary, when a disc with moment of inertia I1 and angular velocity w0 is attached to another disc with moment of inertia I2, they achieve a combined angular velocity of w due to friction between the discs. To find the combined angular velocity, we use the conversion of angular momentum, where the initial angular momentum is I1w0 and the final angular momentum is (I1+I2)w. To calculate the loss of energy, we use the formula 1/2I1w0^2-1/2(I1+I2)w^2. Assuming the discs rotate about the same axis, this is the correct approach.
  • #1
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a disc with moment of inertia I1 turns around its axis which passes through its centre with an angular velocity of w0. we attach to it another disc with moment of inertia I2 (at first it doesn't spin), as a result of friction between the discs they achieve a combined angular velocity of w.
i need to find the combined angular velocity, w?
how much mechanical velocity was lost in the process.

basically i think i need to use here conversion of angular momentum, i.e the a.m before is I1w0, my problem is what the angular momentum after we add the second disc, i think it's I2w+I1w am i correct here?
if so then I1w0=(I1+I2)w.
and to calculate the loss of energy we have:
1/2I1w0^2-1/2(I1+I2)w^2, right?
 
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  • #2
Assuming they rotate about the same axis, yes you are correct.
 
  • #3
yes they rotate about the same axis.
 

1. What is angular momentum?

Angular momentum is a measure of the rotational motion of an object. It is a vector quantity that takes into account the mass, speed, and distance from the axis of rotation of an object.

2. How is angular momentum calculated?

Angular momentum is calculated by multiplying the moment of inertia of an object (a measure of its resistance to rotational motion) by its angular velocity (the rate at which it rotates around an axis).

3. What is the relationship between angular momentum and torque?

Angular momentum and torque are related through the principle of conservation of angular momentum. This principle states that the total angular momentum of a system remains constant unless acted upon by an external torque. This means that if the torque acting on a system is zero, the angular momentum will remain constant.

4. How does the moment of inertia affect angular momentum?

The moment of inertia directly affects the angular momentum of an object. The greater the moment of inertia, the more resistance there is to changes in angular velocity, and therefore, the greater the angular momentum. This is why it is easier to rotate a lightweight object compared to a heavier one.

5. Can angular momentum be transferred between objects?

Yes, angular momentum can be transferred between objects through collisions or interactions between them. For example, when two objects collide, the angular momentum of one can be transferred to the other, resulting in changes in their rotational motion.

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