When is rotational energy conserved?

AI Thread Summary
In the discussion, participants explore the conservation of energy and angular momentum in a problem involving skaters rotating around a fixed point after one stops abruptly. The initial kinetic energy of the skaters does not equal the final rotational energy, leading to confusion about energy conservation. It is clarified that angular momentum is conserved in this scenario, while energy is not due to external forces acting on the system. A comparison is made to another problem where potential energy converts to rotational kinetic energy, highlighting the need to recognize when energy conservation applies. Understanding the conditions under which these principles hold is crucial for solving similar physics problems.
Jimmy25
Messages
69
Reaction score
0

Homework Statement



Four 60 kg skaters join hands and skate down an ice rink at 4.6 m/s. Side by side, they form a line 6 m long. The skater at one end stops abruptly, and the line proceeds to rotate rigidly about that skater. Find the linear speed of the outermost skater.

The Attempt at a Solution



What I did was equate the initial kinetic with the final rotational energy. This does not jive with the answer and the solutions say to use conservation of angular momentum.

Why isn't energy conserved?
 
Physics news on Phys.org
I take this problem, and see it as a rigid rod partitioned into 4 parts; one for each skater.

A force is exerted at the center of the right-most partition. The force on the rod changes the kinetic energy of the rod. So energy is not conserved.

As this force is applied 3/8ths of the rod's length from its center of mass, angular momentum is not conserved.
 
Last edited:
Another question involves a rod which is initially standing on end. It tips over with the bottom of the rod attached to the ground. In this case all the potential energy of the rod is converted to rotational kinetic energy.

How can I distinguish between these two types of problems? (ie how do I recognize when I can use conservation of energy). They both effectively involve a rotating rod about a fixed axis.
 
Jimmy25 said:
Another question involves a rod which is initially standing on end. It tips over with the bottom of the rod attached to the ground. In this case all the potential energy of the rod is converted to rotational kinetic energy.

How can I distinguish between these two types of problems? (ie how do I recognize when I can use conservation of energy). They both effectively involve a rotating rod about a fixed axis.

You seem to have gotten this one. Potential energy is converted to kinetic energy.
 
Yes, I did get that one. However I didn't get the first one because I don't understand how energy is conserved in one but not in the other.

What is the difference?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

What's the source of increase in rotational energy of carousel?
Replies
9
Views
2K
Conservation of Angular Momentum: Hopping onto a Board
Replies
11
Views
2K
Angular momentum: rotating ice skaters
Replies
14
Views
2K
Rotational kinetic energy of ice skater
Replies
6
Views
3K
Conservation of angular momentum and rotational kinetic energy
Replies
2
Views
1K
Solving Rotating Ice Skaters Problem: Is their Straight Line Parallel?
Replies
7
Views
2K
Rotational kinematic need explanation
Replies
7
Views
1K
How Do Skaters' Velocities Change After Grabbing a Pole?
Replies
1
Views
5K
Question about springs and rotational/translational energy
Replies
4
Views
1K
Elastic Collision in Two Reference Frames
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top