Angular Velocity from KE, radius, and mass

In summary: The moment of inertia is not just mr^2. You have to integrate mr^2 over the length of the rod. Look it up.I don't understand what you mean by "integrate mr^2 over the length of the rod." I looked it up and I can't find anything. Would the units for the moment of inertia be kg*m^2?In summary, the problem involves a 45-cm-long, 95 g uniform rod rotating about an axle at one end, with a given amount of rotational kinetic energy. The relevant equation for this problem is KE=(1/2)Iω^2. The moment of inertia for a uniform rod is not just mr^2, but must be integrated over the
  • #1
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Homework Statement
A 45-cm-long, 95 g rod rotates about an axle at one end of the rod. At what angular velocity, in rpm , does the rod have 50 mJ of rotational kinetic energy?
Relevant Equations
Not given
I tried using the equation w^2 = (4*K)/(mr^2) but I don't think this is right... I got my answer to be 3.2243 and that's not correct
 
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  • #2
aivilo775 said:
Homework Statement::
A 45-cm-long, 95 g rod rotates about an axle at one end of the rod. At what angular velocity, in rpm , does the rod have 50 mJ of rotational kinetic energy?
Relevant Equations:: Not given

I tried using the equation w^2 = (4*K)/(mr^2) but I don't think this is right... I got my answer to be 3.2243 and that's not correct
Hello @aivilo775 ,

:welcome:

Under Relevant Equations, you should supply whatever equations are relevant to your problem, such as: ##KE=(1/2)I\omega^2##
for the problem you posted.

Also of importance is what you use to get the moment of inertia, ##I## .

You need to be more detailed as to how you obtained your result. Also be careful with units and define symbols.
 
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  • #3
Screen Shot 2022-10-26 at 9.54.32 PM.png

This is the math I did when I rearranged
Screen Shot 2022-10-26 at 9.54.47 PM.png
to solve for w, angular velocity. I used I = mr^2. I got w = 2.27995. The units would be the sqrt of(J /kg*m^2), which ends up just being 1/sec. to get the answer in rpm, I figured I would multiply w by 60sec (to get w = 136.797, but this wasn't right
 
  • #4
Please use LaTeX to write your equations in symbolic form. It is not at all clear what the numbers you posted in #3 are all about. Also, what is the moment of inertia of the rod? Look it up.
 
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  • #5
aivilo775 said:
I used I = mr^2
It's a uniform rod, not a point mass.
 
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1. What is angular velocity and how is it related to kinetic energy, radius, and mass?

Angular velocity is a measure of the rate of change of rotational displacement. It is related to kinetic energy, radius, and mass through the equation: ω = √(2KE/mr^2), where ω is angular velocity, KE is kinetic energy, m is mass, and r is radius.

2. How do changes in kinetic energy, radius, and mass affect angular velocity?

Changes in kinetic energy, radius, and mass can directly affect angular velocity. An increase in kinetic energy or radius will result in an increase in angular velocity, while an increase in mass will result in a decrease in angular velocity.

3. Can angular velocity be negative?

Yes, angular velocity can be negative. A negative angular velocity indicates that the object is rotating in the opposite direction of the chosen axis of rotation.

4. How is angular velocity measured?

Angular velocity is typically measured in radians per second (rad/s). It can also be measured in revolutions per minute (rpm) or degrees per second (deg/s).

5. What is the difference between angular velocity and linear velocity?

Angular velocity measures the rate of change of rotational displacement, while linear velocity measures the rate of change of linear displacement. Angular velocity is measured in units of angle per unit time, while linear velocity is measured in units of distance per unit time.

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