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A triangle's rotational kinetic energy problem

  • Thread starter Nadialy
  • Start date
6
0
1. Homework Statement
The three 300 g masses in the figure are connected by massless, rigid rods to form a triangle.
knight_Figure_13_29.jpg


What is the triangle's rotational kinetic energy if it rotates at 8.00 revolutions per s about an axis through the center?

Values given:
Mass of each ball at the corner of the triangle: 0.3 kg
Sides of Equilateral Triangle: 0.4m
It is rotating at 8.00 revolutions per second

2. Homework Equations
I= (m)(r[tex]^{2}[/tex]) + (m)(r[tex]^{2}[/tex]) + (m)(r[tex]^{2}[/tex])
K[tex]_{rot}[/tex]=(1/2)Iw[tex]^{2}[/tex]

3. The Attempt at a Solution

First thing i did was try to find the radius of the triangle. I cut it in half down the middle, making a right angle with a side of .2m and a hypotenuse of .4m.

(0.2[tex]^{2}[/tex]) + (height[tex]^{2}[/tex]) =(0.4[tex]^{2}[/tex])
height = 0.346

I halved the height to get the radius.

Radius: 0.173


Then i used the Equation I= (m)(r[tex]^{2}[/tex]) + (m)(r[tex]^{2}[/tex]) + (m)(r[tex]^{2}[/tex])

I = (0.3)(0.173[tex]^{2}[/tex]) + (0.3)(0.173[tex]^{2}[/tex]) + (0.3)(0.173[tex]^{2}[/tex])

I = 0.027

Then i converted 8 rev per sec into 50.24 rad per sec.

Then i used K[tex]_{rot}[/tex]=(1/2)Iw[tex]^{2}[/tex]

K[tex]_{rot}[/tex]=(1/2)(0.027)(50.24)[tex]^{2}[/tex]

K[tex]_{rot}[/tex] = 136

I don't know what I'm doing wrong. Please help.
 

Answers and Replies

Dick
Science Advisor
Homework Helper
26,258
618
The radius of rotation isn't 0.173m. Think about it. It's the hypotenuse of a triangle, one of whose sides is 0.2m. It should be the distance from the center of the triangle to the rotating masses, not the "height".
 
Last edited:
6
0
wouldn't that be .4 then? I don't think I understand what you're trying to tell me.
 
Dick
Science Advisor
Homework Helper
26,258
618
The 'r' in your formula should be the distance from the axis to the rotating masses. It isn't 0.173m nor is it 0.4m. Rethink your triangle.
 
6
0
Thank you. That was a silly place for me to make mistakes.
 

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