Relate rotational kinetic energy to potential energy

In summary, the potential energy of the bar changes when it goes from horizontal to vertical. The change in height should be L/2, not L, because that's how much the potential energy gets changed.
  • #1
lydia_y620
8
1

Homework Statement


This problem is from the 2015 AP Physics C Mechanics free response, question 3 part b.
https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_frq_physics_c-m.pdf
upload_2017-4-15_2-49-11.png


Homework Equations


K = 1/2Iω2
U = mgh

The Attempt at a Solution


The potential energy of the bar when it's horizontal gets transferred to kinetic energy when vertical, so I originally had the equation mgL = 1/2(1/3ML22
However, the scoring guidelines say that the change in height should be L/2, not L, resulting in a potential energy of mgL/2. Could someone explain why the change in height should be L/2 and not L?
 
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  • #2
The change in vertical position of the end of the bar is L. Is that the point that's important in the problem?
 
  • #3
vela said:
The change in vertical position of the end of the bar is L. Is that the point that's important in the problem?
It asks for the velocity of the "free end of the rod", so I think that it means the end of the bar. But why does the answer sheet say L/2 then?
 
Last edited:
  • #4
Is that relevant to the change in potential energy of the rod? Why not use the position of the other end or a point 1/3 the way in from one end? I'm trying to get you to think about what point is important when you talk about the potential energy of the rod.
 
  • #5
vela said:
Is that relevant to the change in potential energy of the rod? Why not use the position of the other end or a point 1/3 the way in from one end? I'm trying to get you to think about what point is important when you talk about the potential energy of the rod.
So I have to take the entire bar into account and not just the end...kind of like taking the "average" change in height for all pieces of the rod?
 
  • #6
Yes. More precisely, the average position of the mass of the bar, i.e., the center of mass.
 
  • #7
vela said:
Yes. More precisely, the average position of the mass of the bar, i.e., the center of mass.
Okay, that makes sense. Thanks for the help!
 

Related to Relate rotational kinetic energy to potential energy

What is rotational kinetic energy and potential energy?

Rotational kinetic energy is the energy possessed by a rotating object due to its motion. Potential energy is the energy stored in an object due to its position or configuration.

How are rotational kinetic energy and potential energy related?

Rotational kinetic energy and potential energy are related through the principle of conservation of energy. As an object rotates, it converts its potential energy into kinetic energy and vice versa.

How do we calculate rotational kinetic energy and potential energy?

Rotational kinetic energy is calculated using the formula 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity. Potential energy is calculated using the formula mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.

What are some real-life examples of rotational kinetic energy and potential energy?

One example is a rollercoaster, where the potential energy of the cars at the top of the track is converted into kinetic energy as they go down the track. Another example is a swinging pendulum, where the potential energy at the highest point is converted into kinetic energy at the lowest point.

How is the concept of rotational kinetic energy and potential energy applied in different fields such as engineering and physics?

In engineering, understanding the relationship between rotational kinetic energy and potential energy is important in designing machines and structures that involve rotational motion. In physics, it is used to explain the behavior and dynamics of rotating objects, such as planets and satellites.

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