Calculating Kinetic Energy of a Rotating Grinding Wheel

In summary, the conversation discussed calculating the kinetic energy of a rotating grinding wheel and determining the height from which it would need to be dropped in order to acquire this kinetic energy. The formula for kinetic energy was used and the value for height was calculated to be 5 meters. The conversation also touched on the concept of energy transformations and the use of the formula for gravitational potential energy. The question was not posted verbatim, but the solution was provided.
  • #1
physaru86
13
0
1. A grinding wheel of mass 5 kg and diameter 0.20 m is rotating with an angular speed of 100 rad/s. Calculate its kinetic energy. Through what distance would it have to be dropped in free fall to acquire this kinetic energy? m = 5 kg, r = 0.20/2 m = 0.10 m, g = 10 m/s2, ω = 100 rad/s 2. v = r*ω, kinetic energy = (1/2)*m*v2

3. v = (0.10 m)*(100 rad/s) = 10 m/s, kinetic energy = (1/2)*(5 kg)*(10 m/s)2 = 250 kgm2/s2..... is this right?

 
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  • #2
Yes it is. Just calculate the second part, it should be easy for you now.
 
  • #3
PWiz said:
Yes it is. Just calculate the second part, it should be easy for you now.
what formula to use?
 
  • #4
Do you know the formula for gravitational potential energy?
 
  • #5
PWiz said:
Do you know the formula for gravitational potential energy?
U = m*g*h...?
 
  • #6
Correct. Now for what value of ##h## does this expression equal 250 joules?
 
  • #7
PWiz said:
Correct. Now for what value of ##h## does this expression equal 250 joules?
um... is it a question or are you helping me with the solution..?
 
  • #8
physaru86 said:
um... is it a question or are you helping me with the solution..?
We don't provide direct answers to homework questions here. And I wouldn't be posting in this thread trying to help you if I didn't know the concept myself :)
 
  • #9
PWiz said:
We don't provide direct answers to homework questions here. And I wouldn't be posting in this thread trying to help you if I didn't know the concept myself :)
Is it related to
Energy conservation during free-fall
 
  • #10
Not exactly. It is more to do with energy transformations. The question is simply asking you from which height you'd have to drop this mass for it to have the same kinetic energy when it's about to strike the surface as the value you have calculated (that's what I think the question is asking, since it appears that the question has not been posted verbatim).
 
  • #11
PWiz said:
Correct. Now for what value of ##h## does this expression equal 250 joules?
m = 5 kg, g = 10 m/s2, m*g*h = 250 joules, h = 250/5*10 m, h = 5 m... ?
 
  • #12
physaru86 said:
m = 5 kg, g = 10 m/s2, m*g*h = 250 joules, h = 250/5*10 m, h = 5 m... ?
That's right.
 
  • #13
PWiz said:
That's right.
So the problem is solved, right...? thanks
 
  • #14
Your welcome :wink:
 

What is a rigid body?

A rigid body is a physical object that maintains its shape and size, even when subjected to external forces. This means that the distances between different points on the object remain constant.

What is rigid body motion?

Rigid body motion refers to the movement of a rigid body as a whole, where all points on the body move in the same direction and at the same speed. This type of motion is often described using translation and rotation.

What is the difference between translation and rotation in rigid body motion?

Translation is when a rigid body moves in a straight line, with all points on the body moving in the same direction and at the same speed. Rotation is when a rigid body turns or spins around a fixed axis, with different points on the body moving at different speeds and in different directions.

What is the formula for calculating the velocity of a rigid body?

The formula for calculating the velocity of a rigid body is v = ω x r, where v is the linear velocity, ω is the angular velocity, and r is the distance from the axis of rotation to the point on the body.

How does the concept of inertia relate to rigid body motion?

Inertia is the tendency of an object to resist changes in its motion. In rigid body motion, the moment of inertia is used to describe how difficult it is to change the rotational motion of a rigid body. The larger the moment of inertia, the harder it is to change the rotation of the body.

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