Angular speed uniform rod problem

In summary, we are tasked to determine the angular speed of a 4.0 m long rod as it passes through the horizontal position. The rod is initially at rest at an angle of 40° above the horizontal and can pivot about a frictionless pin. Using the principle of conservation of energy, we can determine the rotational kinetic energy of the rod at both the initial and final positions, assuming free-fall acceleration to be 9.83 m/s2.
  • #1
tigerlili
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Homework Statement



The thin uniform rod in Fig. 10-52 has length 4.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest at angle θ = 40° above the horizontal. Use the principle of conservation of energy to determine the angular speed of the rod as it passes through the horizontal position. Assume free-fall acceleration to be equal to 9.83 m/s2.



Homework Equations



i really have no idea where to start this :/

The Attempt at a Solution

 
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  • #2
Well the question says to use the law of conservation of energy.

Since we are talking energy and rotation, rotational kinetic energy should be in your energy equation.


At the angle of 40 degrees, when just held at that position (such that it is at rest), what type of energy does it possess? When it passes through the horizontal plane, what type of energy does it have?
 
  • #3
thanks for your help, i actually got it :)
 

1. What is the Angular Speed Uniform Rod Problem?

The Angular Speed Uniform Rod Problem is a physics problem that involves calculating the angular speed of a rod that is rotating about a fixed axis. The rod is assumed to have a uniform mass distribution, meaning that the mass is evenly distributed along its length.

2. How is the angular speed of a uniform rod calculated?

The angular speed of a uniform rod can be calculated using the formula ω = v/R, where ω is the angular speed, v is the linear speed of a point on the rod, and R is the distance from the point to the axis of rotation. This formula is based on the relationship between linear and angular speed: ω = v/r, where r is the radius of the circular path.

3. What is the difference between angular speed and linear speed?

Angular speed refers to the rate of change of angular displacement, while linear speed refers to the rate of change of linear displacement. In other words, angular speed measures how fast an object is rotating, while linear speed measures how fast an object is moving in a straight line.

4. Can the angular speed of a uniform rod change over time?

Yes, the angular speed of a uniform rod can change over time if there is a net torque acting on the rod. Torque is a force that causes an object to rotate, and if there is a net torque acting on a uniform rod, it can cause the rod to speed up or slow down.

5. Are there any real-world applications of the Angular Speed Uniform Rod Problem?

Yes, the Angular Speed Uniform Rod Problem has many real-world applications, such as in the design of rotating machinery, such as engines and turbines. It is also used in the study of rotational motion in physics and engineering.

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