Angular velocity of rod and bug

In summary, the change in angular velocity, w(f), can be calculated by taking the given moment of inertia, I(i), and multiplying it by the initial angular velocity, w(i), and adding it to the product of the mass, m, and the square of the radius, r, plus the initial moment of inertia, I(i). Then, w(f) can be found by dividing the resulting product by the sum of I(i) and the initial angular velocity, w(i). However, if the given moment of inertia is taken as being about the rod's center, the change in angular velocity will be negative.
  • #1
p37
4
1
Homework Statement
A thin rod has a length of 0.138 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.221 rad/s and a moment of inertia of 1.08 x 10-3 kg·m2. A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod?
Relevant Equations
Lfinal = Linitial
L=Iw
I(i)w(i)= I(f)w(f)

I(i)= 1.08 x 10-3 kg·m2
w(i)= 0.221 rad/s
I(f)= mr^2 + I(i) = (5 x 10^-3)(.138)^2 + (1.08 x 10^-3)

(1.08 x 10-3)(.221) = ((1.08 x 10^-3)+9.22 x 10^-5))w(f)

w(f) = (2.3868 x 10^-4)/(0.00117522)

w(f)= 0.203094 rad/s

This is my attempt; however, I cannot seem to get it right. Any help on what I am doing wrong?
 
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  • #2
What answer did you put in?
Note it says "what is the change in"
 
  • #3
I put in 0.203094 but it's wrong
I thought maybe it was .221 - 0.203094 which is .017906 which isn't right either
could it be the negative of that?

I only have one attempt left
 
  • #4
I don't like the fact that it specifies the "moment of inertia " of the rod without stating the axis for that. You are left to guess whether it means about the rod's mass centre or about the given axis of rotation.
You are quoting too many decimal places in your answers, so that's another possibility, but most systems don’t police that.
I haven't checked your arithmetic. I will now.

Update: I agree with your numbers.
 
  • #5
Yeah, I am not sure. I followed videos online with similar problems and they did it the same way. Usually, I don't have an issue with sig figs or decimal points on my program.
 
  • #6
p37 said:
Yeah, I am not sure. I followed videos online with similar problems and they did it the same way. Usually, I don't have an issue with sig figs or decimal points on my program.
I can only suggest you either try -.0179 or take the given MoI as being about the rod's centre.
 
  • #7
The negative was right. Thank you!
 
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What is angular velocity?

Angular velocity is the rate of change of angular displacement of an object with respect to time. It is a measure of how fast an object is rotating.

How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angular displacement by the change in time. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

What is the difference between angular velocity and linear velocity?

Angular velocity is a measure of how fast an object is rotating, while linear velocity is a measure of how fast an object is moving in a straight line. Angular velocity is typically measured in radians per second (rad/s) or degrees per second (deg/s), while linear velocity is measured in meters per second (m/s) or feet per second (ft/s).

How does the length of a rod affect its angular velocity?

The length of a rod does not directly affect its angular velocity. However, a longer rod may have a higher linear velocity at the same angular velocity as a shorter rod due to the increased distance traveled in the same amount of time.

Why is the angular velocity of a bug on a rotating rod constant?

The angular velocity of a bug on a rotating rod is constant because the bug is moving in a circular path at a constant distance from the center of rotation. This means that the bug is traveling the same distance in the same amount of time, resulting in a constant angular velocity.

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