What is the Angular Acceleration of a Free-Rotating Rod at a Specific Angle?

In summary, the conversation is about a uniform rod with a mass of 2.0 kg and a length of 0.60m that is free to rotate around a frictionless pivot at one end. The question is asking for the magnitude of the angular acceleration of the rod when it is released from rest in the horizontal position and is at 60 degrees below the horizontal. The person asking for help is advised to calculate the moment of inertia and torque of the rod in order to find the angular acceleration using Newton's second law for rotation. They are also encouraged to show their work and use appropriate formulas.
  • #1
rlmurra2
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A uniform rod (mass=2.0 kg, length=.60m) is free to rotate about a frictionless pivot at one end. The rod is released from rests in the horizontal position. What is the magnitude of the angular acceleration of the rod at the instant it is 60 degrees below the horizontal?

Please help! I really need this one!
 
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  • #2
rlmurra2 said:
A uniform rod (mass=2.0 kg, length=.60m) is free to rotate about a frictionless pivot at one end. The rod is released from rests in the horizontal position. What is the magnitude of the angular acceleration of the rod at the instant it is 60 degrees below the horizontal?

Please help! I really need this one!
You should show us your attempt to solve this problem, then ask for help

https://www.physicsforums.com/showthread.php?t=4825

In case you have no idea where to get started, you need to calculate the moment of inertia of a rod pivoting at one end. You might find that by looking it up, or by using the parallel axis theorem after looking up the moment of inertia of a rod rotating about its center. Then you will need to calculate the torque acting on the rod about the pivot point. This torque comes from the force of gravity acting at the center of the rod. Then you will use "Newton's second law for rotation" to find the angular acceleration as the ratio of the torque to the moment of inertia.
 
  • #3
Please show some work, such as the appropriate formula for calculating angular momentum as a function of the position (angle) of a rod pivoting at one end.
 

FAQ: What is the Angular Acceleration of a Free-Rotating Rod at a Specific Angle?

What is Angular Acceleration?

Angular acceleration is the rate of change of angular velocity over time. It measures how quickly an object's rotational speed is changing.

How is Angular Acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is: α = (ωf - ωi) / t, where α is angular acceleration, ωf is final angular velocity, ωi is initial angular velocity, and t is time.

What is the unit of measurement for Angular Acceleration?

The unit of measurement for angular acceleration is radians per second squared (rad/s²).

How does Angular Acceleration relate to Linear Acceleration?

Angular acceleration and linear acceleration are related through the formula a = rα, where a is linear acceleration, r is the radius of the circular motion, and α is angular acceleration. This formula shows that an increase in angular acceleration will result in a greater linear acceleration.

What factors affect Angular Acceleration?

The factors that affect angular acceleration include the applied torque, the moment of inertia, and any external forces acting on the rotating object. Additionally, the shape and size of the object and the distribution of its mass can also affect angular acceleration.

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