Rotation of Rigid Body

In summary, a metre rule is freely pivoted about its centre and a piece of mud of mass 20g traveling at 5ms-1 strikes and sticks to one end, causing the rule to rotate in a horizontal circle. The moment of inertia of the rule and mud about the pivot is 0.02kgm^2. After calculating with the assumption that the momentum of the mud is transferred solely to the angular momentum, the initial angular velocity of the rule is found to be 5 rads-1. However, upon further consideration, the assumption may be incorrect and further attempts should be made using units in meters, kilograms, and seconds.
  • #1
Harmony
203
0
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?
 
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  • #2
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
 
Last edited:
  • #3


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.
 

1. What is rotation of a rigid body?

Rotation of a rigid body is the movement of an object around an axis or point, where all points of the object move in a circular motion at the same time and with the same angular velocity.

2. How is rotation of a rigid body different from translation?

Rotation involves movement around an axis or point, while translation involves movement in a straight line. In rotation, all points of the object move in a circular motion, while in translation, the object moves as a whole in a straight line.

3. What is the importance of studying rotation of a rigid body?

Understanding the principles of rotation of a rigid body is important in many fields, such as engineering, physics, and mechanics. It helps in predicting the behavior of objects under rotational motion, designing structures that can withstand rotational forces, and solving complex problems involving rotational motion.

4. How is angular velocity related to rotation of a rigid body?

Angular velocity is the measure of how fast an object is rotating around an axis or point. It is directly proportional to the rotational speed of a rigid body, and can be used to calculate the change in angular displacement over time.

5. What are some real-life examples of rotation of a rigid body?

Some common examples of rotation of a rigid body include a spinning top, a rotating fan, a swinging pendulum, and a Ferris wheel. In sports, throwing a ball, swinging a bat, and spinning a discus are all examples of rotational motion. In nature, the rotation of Earth on its axis and the orbit of planets around the sun are also examples of rotation of rigid bodies.

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