Initial Acceleration of a Center of Mass

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SUMMARY

The discussion focuses on calculating the initial acceleration of the center of mass of a uniform rod of length 1.25 m, released from a 23.0° angle above the horizontal. The center of mass is located at 0.625 m (1/2 * L) from the pivot. The torque due to gravity is calculated to determine the angular acceleration, which is then related to the linear acceleration of the center of mass using the formula αD = a, where D is the distance to the center of mass. The correct approach involves understanding the relationship between torque, angular acceleration, and linear acceleration.

PREREQUISITES
  • Understanding of torque and its calculation
  • Knowledge of angular acceleration and its relation to linear acceleration
  • Familiarity with the concept of center of mass in rigid bodies
  • Basic principles of rotational dynamics
NEXT STEPS
  • Study the calculation of torque in rigid body dynamics
  • Learn about the relationship between angular acceleration and linear acceleration
  • Explore the concept of center of mass in various geometries
  • Review the principles of rotational motion and dynamics
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of rigid bodies, particularly in the context of rotational motion and acceleration calculations.

mparsons06
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Homework Statement



A uniform rod of length 1.25 m is attached to a frictionless pivot at one end. It is released from rest from an angle θ = 23.0° above the horizontal.

PivotRod.gif


Find the magnitude of the initial acceleration of the rod's center of mass.


I keep getting the wrong answer. Please help with a push in the right direction.
 
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You can use the fact that the center of mass lies at 1/2 * L and that gravity grips the rod here. You can then use a simple geometric rule to find the force perpendicular to the rod, hence its initial acceleration.
 
You can calculate the torque exerted by gravity, and hence the angular acceleration of the rod. This can be related to the linear acceleration (of for instance the CoM) by the formula
\alpha D = a
where D is the distance to the point of interest (CoM in this example)
 

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