Rotational motion, energy conservation problem

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SUMMARY

The discussion centers on a physics problem involving a uniform rod and a point mass, where the rod pivots from one end and falls under gravity. Given a mass M of 2 kg and a length L of 2 m, the point mass m of 1 kg is positioned at the tip of the rod, initially at a 30-degree angle. The calculated speed of the tip when the rod is horizontal is incorrectly derived as 4.42 m/s, while the correct answer is 4.8 m/s. The problem also involves calculating the rotational kinetic energy and the total change in gravitational potential energy during the fall.

PREREQUISITES
  • Understanding of rotational motion principles
  • Familiarity with gravitational potential energy (PE) and kinetic energy (KE) equations
  • Knowledge of trigonometric functions, specifically sine
  • Ability to apply conservation of energy concepts in physics
NEXT STEPS
  • Review the derivation of rotational kinetic energy for rigid bodies
  • Study the conservation of mechanical energy in rotational systems
  • Learn about the effects of pivot points on the motion of rigid bodies
  • Explore the relationship between angular displacement and linear velocity in rotational motion
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Students preparing for physics exams, particularly those focusing on rotational dynamics and energy conservation principles.

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rotational motion, energy conservation problem URGENT please help

Homework Statement



A uniform rod of mass M=2 kg and length L = 2m is pivoted from its end. It has a point mass m=1 kg on its tip. It stars from rest at an angle of 30 degrees above horizontal. It falls under the influence of gravity. How fast is the tip m moving when the rod is horizontal at θ
= 0

Homework Equations



mgh = 1/2mv^2

The Attempt at a Solution



h= Lsinθ = 1
m cancels from both sides
so you're left with
v=√2g=4.42

BUT, the actual answer given is 4.8

Help please! I have a test in just a few hours and have been trying to figure this problem out for awhile! Thanks
 
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How would you write the rotational KE of the system? Also, what's the total change in gravitational PE as it falls?
 

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