Rotating Rigid Body Homework: Find Angular Velocity

In summary, the problem involves two masses attached to a thin bar, free to rotate around a horizontal axis. A drop of wax falls on one of the masses and sticks to it. The goal is to retrieve the angular velocity of the system immediately after the impact, but without the mass of the wax drop, it cannot be determined. The inertia moment for a thin bar can be used to solve the problem, but without the wax drop mass, the solution would be in terms of 'm'.
  • #1
Faefnir
10
0

Homework Statement



Two masses of 2 kg are attached to the extremities of a 5 cm long, negligible mass and thin bar, free to rotate around a horizontal axis passing through its center. A drop of wax falls on one of the two masses at ##v = 3 \frac{m}{s}## and sticks to it. Retrieve the angular velocity of the system immediately after the impact

Homework Equations


[/B]
Angular moment:
$$ L = I \cdot \omega $$
$$ L = rp = rmv $$
Inertia moment:
$$ I = (M + M + m) \cdot r^2 $$

The Attempt at a Solution



I don't know if the wax drop mass was deliberately omitted in the text, but if so, how can I get it? Without that I can not get ## \omega ##. I know I should do some attempt, but the only thing that comes to mind is the inertia moment for a thin bar

$$ I_{MC} = \frac{1}{12} m \cdot l^{2} $$

Can you help me? Thanks in advance
 
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  • #2
Faefnir said:
I don't know if the wax drop mass was deliberately omitted in the text, but if so, how can I get it?
You'll need the mass of the wax drop to solve this. Where did you get the problem?
 
  • #3
An italian homework book. Indeed the latest edition dates back to 2003
 
  • #4
Oh well. Without the mass the best you can do is solve things in terms of 'm', but that's clearly not the intention since quantities are given for everything else.
 
  • Like
Likes Faefnir
  • #5
Thank you! You have confirmed that I understand the subject well :D
 

1. What is angular velocity and how is it related to rotating rigid bodies?

Angular velocity is a measure of how quickly a rigid body is rotating around a fixed axis. It is typically represented by the Greek letter omega (ω) and is measured in radians per second. It is related to rotating rigid bodies because it describes the rate of change of the angular displacement of the body.

2. How do you calculate angular velocity for a rotating rigid body?

The formula for angular velocity is ω = Δθ/Δt, where Δθ represents the change in angular displacement and Δt represents the change in time. This formula can also be written as ω = 2πf, where f is the frequency of rotation in hertz.

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

Angular velocity is a measure of how quickly a rigid body is rotating, while linear velocity is a measure of how quickly an object is moving in a straight line. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

4. How does the moment of inertia affect the angular velocity of a rotating rigid body?

Moment of inertia is a measure of how resistant a rigid body is to changes in its rotational motion. The larger the moment of inertia, the slower the angular velocity will be for a given torque. This means that a body with a larger moment of inertia will require more torque to achieve the same angular velocity as a body with a smaller moment of inertia.

5. How is angular velocity used in real-world applications?

Angular velocity is used in a variety of real-world applications, such as understanding the motion of spinning objects like tops and gyroscopes, analyzing the rotation of planets and stars, and designing rotating machinery like turbines and engines. It is also crucial in fields such as robotics, aerospace engineering, and sports science.

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