Angular Acceleration of a Pinned Stick

In summary, the conversation is about someone seeking guidance on how to approach a problem and asking for clarification on the concepts involved. The problem involves a rotating stick with given dimensions and determining the angular acceleration at a specific angle. The conversation also references the moment of inertia and the relationship between gravitational force and angular displacement.
  • #1
hughes
8
0
I have no idea how to approach this problem. I'm not even sure if my visualization is right. Where do I start? Somebody please guide me; I'm not asking for a step by step solution to the answer. I just want to know how to do it.
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A thin, uniform stick of length 2 m and mass 3.4 kg is pinned through one end and is free to rotate. The stick is initially hanging vertically and at rest. You then rotate the stick so that you are holding it horizontally. You release the stick from that horizontal position. What is the magnitude of the angular acceleration of the stick when it has traveled 22.7 degrees (the stick makes an angle of 22.7 degrees with the horizontal)?
Remember that the moment of inertia for a stick of mass m and length L about its end is (1/3)m L^2.
 
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  • #2
The angle between the gravitational force vector and the translational displacement vector (of a given element of the stick) depends on the angular displacement of the stick. Think of how you might be able to take that fact and the given moment of inertia to derive two different equations for the torque due to gravity.
 

FAQ: Angular Acceleration of a Pinned Stick

What is angular acceleration of a pinned stick?

Angular acceleration of a pinned stick is the rate at which the angular velocity of the stick changes over time. It is a measure of how quickly the stick is rotating around a fixed point, or pivot, known as the pin.

How is angular acceleration of a pinned stick calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. In other words, it is the slope of the angular velocity vs. time graph.

What factors affect the angular acceleration of a pinned stick?

The angular acceleration of a pinned stick is affected by the applied torque, or rotational force, and the moment of inertia of the stick. A higher torque or a lower moment of inertia will result in a greater angular acceleration.

What are the units of angular acceleration?

The units of angular acceleration are radians per second squared (rad/s^2) in the SI system and degrees per second squared (deg/s^2) in the imperial system.

What is the difference between angular acceleration and linear acceleration?

Angular acceleration is a measure of how quickly an object is rotating, while linear acceleration is a measure of how quickly an object is changing its linear velocity. Angular acceleration is expressed in radians per second squared, while linear acceleration is expressed in meters per second squared.

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