Pivoting Bar and Kinetic Energy

In summary, a 12.0kg bar that is 2.00m long rotates uniformly about a pivot at one end, making 5.00 complete revolutions every 3.00 seconds. To find the kinetic energy of the bar, the integral of v^2 dm is used, where dm is equal to (M/L)*dx. However, it is unclear how to integrate this as velocity is not constant and not in terms of dm. Attempting to integrate in terms of dx by rewriting the integral as K= 1/2 * (2Pi/t)^2 * M/L * integral x^2 dx may not be the correct approach. The integration is still unclear, especially considering the 5.00 revolutions in
  • #1
DanielB
1
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Homework Statement



A thin, uniform 12.0kg bar that is 2.00m long rotates uniformly about a pivot at one end, making 5.00 complete revolutions every 3.00 seconds.

What is the kinetic energy of this bar? (Hint: Different points in the bar have different speeds. Break the bar up into infinitesimal segments of mass dm and integrate to add up the kinetic energy of all these segments.)

Homework Equations



K = 1/2 integral of v^2 dm
dm = (M/L)*dx

The Attempt at a Solution



I was confused on how to integrate this particular integral as velocity is not a constant and is clearly not in terms of dm. I attempted to integrate in terms of dx rewriting the integral as:

K= 1/2 * (2Pi/t)^2 * M/L integral x^2 dx

I don't think that is the correct direction but I am generally confused with the integration.
[EDIT]: Template was incorrect
 
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  • #2
I don't see where your velocity takes into account the 5.00 revolutions it does in t=3.00 seconds.
 

FAQ: Pivoting Bar and Kinetic Energy

1. What is a pivoting bar?

A pivoting bar is a rigid object that is attached to a fixed point and can rotate around that point. It is commonly used in physics to demonstrate principles of torque and rotational motion.

2. How does a pivoting bar work?

A pivoting bar works by applying a force at a distance from the fixed point, creating a torque that causes the bar to rotate around that point. This rotation can be described using principles of rotational motion, such as angular velocity and angular acceleration.

3. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is defined as one-half of the mass of the object multiplied by the square of its velocity. Kinetic energy is a scalar quantity and is measured in joules (J).

4. How is kinetic energy related to a pivoting bar?

As a pivoting bar rotates, its points of mass also move, which means they possess kinetic energy. The total kinetic energy of the bar can be calculated by adding up the kinetic energy of each point of mass, using the formula 1/2mv^2. This can help us understand the energy conservation and transfer involved in the motion of the bar.

5. Why is understanding the relationship between pivoting bar and kinetic energy important?

Understanding the relationship between a pivoting bar and kinetic energy helps us to understand principles of rotational motion, such as torque and angular momentum. It also has practical applications, such as in designing machines and structures that involve rotational motion, such as doors, wheels, and cranks.

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