Angular Acceleration of a Pinned Stick

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SUMMARY

The discussion focuses on calculating the angular acceleration of a pinned stick when released from a horizontal position after being rotated. The stick has a length of 2 m and a mass of 3.4 kg, with a moment of inertia calculated using the formula (1/3)mL². At an angular displacement of 22.7 degrees from the horizontal, participants are encouraged to derive equations for torque due to gravity, emphasizing the relationship between gravitational force and angular displacement. This problem requires a solid understanding of rotational dynamics and torque calculations.

PREREQUISITES
  • Understanding of rotational dynamics
  • Familiarity with torque and angular acceleration
  • Knowledge of moment of inertia calculations
  • Basic principles of gravitational force
NEXT STEPS
  • Study the derivation of torque equations in rotational motion
  • Learn about angular acceleration and its relation to torque
  • Explore the concept of moment of inertia for various shapes
  • Investigate the effects of angular displacement on torque calculations
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Students and educators in physics, particularly those focusing on mechanics and rotational dynamics, as well as anyone interested in solving problems related to angular motion and torque.

hughes
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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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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.
 

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