- #1
Calculating Kinetic Energy of a Segment: Where Did I Go Wrong?
- Thread starter Saitama
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- Energy Kinetic Kinetic energy
In summary, the conversation discusses an error in the first line of a solution to a physics problem involving angular speed and distance. The correct approach is suggested and the limits for integration are clarified.
- #2
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Your first line is wrong. How did you get 1+sin(θ)? You're measuring it down fron horizontal, so should be minus.
And in the last step, you've evaluated the integral of the sin(θ) part to zero. It won't be.
Another approach is to say the angular speed is v/R and work out the distance from the element to the point of contact.
And in the last step, you've evaluated the integral of the sin(θ) part to zero. It won't be.
Another approach is to say the angular speed is v/R and work out the distance from the element to the point of contact.
- #3
Saitama
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Oh yes, the integral sin(θ) won't be zero. I evaluated it correctly during the examination but did it wrong while posting up my attempt.haruspex said:
I did the necessary corrections as you said and got the right answer. One more question, would the limits for integration change from 0 to -pi?
This approach is much easier. I am not much familiar with the instantaneous axis of rotation but this worked out pretty well. Thanks for the alternate method.haruspex said:
- #4
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No, you're measuring theta anticlockwise in the diagram from the "9 o'clock" position, so it will be 0 to pi.Pranav-Arora said:
- #5
Saitama
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haruspex said:
Got it, thanks haruspex!
FAQ: Calculating Kinetic Energy of a Segment: Where Did I Go Wrong?
What is kinetic energy of a segment?
Kinetic energy of a segment refers to the energy that an object possesses due to its motion. It is a scalar quantity that is dependent on the mass and velocity of the object.
How is kinetic energy calculated?
Kinetic energy is calculated using the equation KE = 1/2 * mv^2, where m is the mass of the object and v is its velocity. This equation is derived from the work-energy theorem.
What are the units of kinetic energy?
The units of kinetic energy are Joules (J) in the SI system. In the imperial system, it is measured in foot-pounds (ft-lb).
What factors affect the kinetic energy of a segment?
The kinetic energy of a segment is affected by its mass and velocity. A heavier object or one with a greater velocity will have a higher kinetic energy compared to a lighter object or one with a lower velocity.
Why is kinetic energy important in physics?
Kinetic energy is important in physics because it is a fundamental concept that is used to explain the behavior of moving objects. It is also a key component in various equations and principles, such as the work-energy theorem and conservation of energy.