Calculating Rotational Energy of Disk After Forces Applied

In summary, a uniform disk with mass 9.32 kg and radius 1.37 m is at rest in the x-y plane with three forces acting in the +y-direction. After 1.5 seconds, the rotational energy of the disk can be calculated using the equation E=1/2*I*ω^2, where ωi is 0 and the values of I and ω can be found using the equations I=1/2*mR^2 and ω=ωi+alpha*t.
  • #1
ctwokay
30
0

Homework Statement



A uniform disk with mass m = 9.32 kg and radius R = 1.37 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 340 N at the edge of the disk on the +x-axis, 2) a force 340 N at the edge of the disk on the –y-axis, and 3) a force 340 N acts at the edge of the disk at an angle θ = 30° above the –x-axis.

Q: If the disk starts from rest, what is the rotational energy of the disk after the forces have been applied for t = 1.5 s?

Homework Equations



I=1/2*mR^2
τ=I*alpha
ω=ωi+alpha*t
E=1/2*I*ω^2


The Attempt at a Solution


I just want to check whether my working is correct or not.

I use ω=ωi+alpha*t which ωi is zero,then i sub in the values to E=1/2*I*ω^2 to find the rotational energy.
Please help me check my workings is it right?
Thank you.
 
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  • #2
hi ctwokay! :smile:

(have an alpha: α and try using the X2 and X2 buttons just above the Reply box :wink:)
ctwokay said:
I=1/2*mR^2
τ=I*alpha
ω=ωi+alpha*t
E=1/2*I*ω^2

I use ω=ωi+alpha*t which ωi is zero,then i sub in the values to E=1/2*I*ω^2 to find the rotational energy.

yes, that's fine! :smile:
 
  • #3
thank you very much
 

FAQ: Calculating Rotational Energy of Disk After Forces Applied

1. How do you calculate the rotational energy of a disk after forces are applied?

To calculate the rotational energy of a disk, you need to know the moment of inertia (I) and the angular velocity (ω). The formula for rotational energy is E = 1/2 x I x ω².

2. What is moment of inertia and how is it related to rotational energy?

Moment of inertia is a measure of an object's resistance to rotational motion. It depends on the mass and distribution of the mass around the axis of rotation. It is related to rotational energy because it is a key factor in calculating the amount of energy an object has due to its rotational motion.

3. Can you provide an example of calculating the rotational energy of a disk?

Sure, let's say we have a disk with a moment of inertia of 2 kgm² and an angular velocity of 10 rad/s. The rotational energy would be calculated as follows: E = 1/2 x 2 kgm² x (10 rad/s)² = 100 Joules.

4. How does friction affect the calculation of rotational energy?

Friction can cause a decrease in the angular velocity of a disk, thus decreasing its rotational energy. This is because friction acts as a resistive force that opposes the motion of the disk, resulting in a loss of energy.

5. Is there a limit to the amount of rotational energy a disk can have?

No, there is no limit to the amount of rotational energy a disk can have. As long as there are forces acting on the disk to keep it rotating, its rotational energy can continue to increase. However, it is important to note that there may be practical limitations due to factors such as material strength and stability.

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