Solving the Problem of Angular Speed After Clay Striking Bar

In summary, the center of mass of the composite system is at the position of the origin, which is the midpoint of the rod.
  • #1
zhenyazh
56
0
Hi
i am preparing for the test and i have a problem with the following question.
an image is attached.

On a frictionless table, a glob of clay of mass 0.30 kg strikes a bar of mass 1.20 kg perpendicularly at a point 0.22 m from the center of the bar and sticks to it.

If the bar is 1.34 m long and the clay is moving at 7.3 m/s before striking the bar, what is the final speed of the center of mass?
this i have found 1.460 m/s

At what angular speed does the bar/clay system rotate about its center of mass after the impact?

i am quite confused here.
can u show me how to solve this.
especially as i know i need to find the distance between my the center of mass and the point with respect to which i calculate - how do i calculate the center of mass.
it is a weighed average between distances from the respect point, but what is the distance of the bar. do i use its length or the distance from one side to the place where the clay is?
 

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  • #2
anyone? :)
 
  • #3
This is an inelastic collision that does not conserve mechanical energy. You need to conserve angular momentum about the center of mass of the rod and linear momentum. Your unknowns are the speed of the center of mass after the collision and the angular speed ω.
 
  • #4
sure, so far i knew i should do it too.
but take a look at the last paragraph of what I've written. i think i am doing the calculation o mention there wrong and this is why i get a wrong result.
 
  • #5
If I understand correctly you want to know how to find the center of mass of the composite system. Don't forget that the rod can be viewed as having its entire mass at its midpoint. This is what you do

1. Define your origin (with respect to which you measure all distances) to be the midpoint of the rod.
2. Let M be the mass of the rod, m be the mass of the glob and d the position of the glob after it is stuck on the rod.

Then the position of the center of mass of the composite is given by

[tex]X=\frac{M \times 0 + m \times d}{M+m}[/tex]

Is this what you were looking for?
 
  • #6
hi
i am still confused.
no matter what i do i can't get the correct result.
could please write the solution outline in parameters? or at least describe
each stage of the solution?

thanks
 

1. What is angular speed and why is it important in this problem?

Angular speed is a measure of how fast an object is rotating around a fixed point. In this problem, it is important because it helps us understand the motion of the clay after it strikes the bar and how it affects the bar's rotation.

2. How can we determine the angular speed of the bar after being struck by the clay?

To determine the angular speed of the bar, we can use the equation ω = Δθ/Δt, where ω is the angular speed, Δθ is the change in angle, and Δt is the change in time. We can measure the change in angle by tracking the position of the bar and the clay before and after the strike, and the change in time can be measured with a stopwatch.

3. What factors can affect the angular speed of the bar after being struck by the clay?

The angular speed of the bar can be affected by various factors, such as the initial velocity and mass of the clay, the distance between the bar and the point of impact, and the moment of inertia of the bar. The surface friction between the clay and the bar can also play a role in determining the angular speed.

4. How can we use this information to solve the problem of angular speed after clay striking bar?

By understanding the factors that affect the angular speed, we can manipulate them to solve the problem. For example, we can adjust the initial velocity or mass of the clay to see how it affects the angular speed of the bar. We can also change the distance between the bar and the point of impact to observe its impact on the angular speed.

5. What are some real-world applications of solving the problem of angular speed after clay striking bar?

Understanding the principles of angular speed can have practical applications in fields such as engineering, robotics, and sports. For example, in engineering, this knowledge can be used to design machines and mechanisms that require precise control of rotation. In sports, it can be used to analyze the speed and movement of rotating objects, such as a basketball being shot into a hoop.

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