How Does Mud Impact the Angular Velocity of a Pivoted Meter Rule?

[Harmony]

A metre rule is freely pivoted about its centre. A piece of mud of mass 20g traveling at 5ms-1 strikes and sticks to one end of the rule so that the rule starts to rotate in a horizontal circle. If the moment of Inertia of the rule and the mud about the pivot is 0.02kgm^2, the initial angular velocity of the rule is...(Answer:2.5rads-1)

I have made assumption that the momentum of the mud is transfer solely to
the angular momentum. (mv=Iw)
I got the answer 5 rads-1, obviously wrong. I believe that my assumption is wrong. How should I attempt this question?

 

[Allday]

mks units

hi harmony

make sure you convert all units to m-> meters, k-> kilograms, and s-> seconds...then you should get the correct answer with your assumption.

ahhh actually I am wrong i was reading your post backwards. i thought 5 rad/s was the correct answer...gonna have to think about this for a little while

gabe

 

[kyle8921]

Your assumption is correct, however, there might be some error in your calculation. Let's break down the steps to solve this problem:

1. We know that the moment of inertia (I) is equal to the mass (m) times the square of the distance from the pivot (r) squared. So, we can calculate the moment of inertia of the rule and the mud as follows:

I = (0.02kg)(0.5m)^2 = 0.005kgm^2

2. We also know that the initial angular momentum (L) is equal to the moment of inertia (I) times the initial angular velocity (w). So, we can rearrange this equation to solve for w:

w = L/I

3. Now, we need to calculate the initial angular momentum. We can do this by using the conservation of momentum principle. This means that the initial momentum of the mud (mv) is equal to the final angular momentum of the rule and the mud (Iw). So, we can set up the following equation:

mv = Iw

4. We can plug in the values we know into this equation, so we get:

(0.02kg)(5ms^-1) = (0.005kgm^2)w

5. Solving for w, we get:

w = (0.02kg)(5ms^-1)/(0.005kgm^2) = 2.5rads^-1

Therefore, the initial angular velocity of the rule is 2.5rads^-1. It seems that your calculation was correct, but you might have made a mistake in the units or in the calculation. I would recommend double-checking your work to find the error.