Solid Ball Problem: Kinetic Energy Calculation

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SUMMARY

The discussion focuses on calculating the kinetic energy of a solid ball with a mass of 1.70 kg and a diameter of 16.0 cm, rotating at 65.0 revolutions per minute (rev/min). The correct formula for kinetic energy in rotational motion is KE = 1/2 * I * ω², where I is the moment of inertia. The moment of inertia for a solid sphere is I = 2/5 * m * r², and the radius must be converted from diameter to meters. Participants emphasized the importance of using correct units and formulas to avoid calculation errors.

PREREQUISITES
  • Understanding of rotational motion and kinetic energy
  • Familiarity with moment of inertia calculations
  • Knowledge of unit conversions (e.g., diameter to radius, rev/min to radians/second)
  • Basic algebra for solving equations
NEXT STEPS
  • Learn about the moment of inertia for different shapes, specifically I = 2/5 * m * r² for solid spheres
  • Study angular velocity conversion from revolutions per minute to radians per second
  • Explore examples of kinetic energy calculations in rotational dynamics
  • Review common mistakes in physics calculations and how to avoid them
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Students studying physics, particularly those focusing on rotational dynamics, as well as educators looking for examples of kinetic energy calculations in solid objects.

envscigrl
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Here is my last problem I am having problems with:
A solid ball of mass 1.70kg and diameter 16.0cm is rotating about its diameter at 65.0rev/min. What is its kinetic energy ?
Ok so KE for rotation is : 1/2*I *w^2
so I found I with m *r2
and then plugged everything into the Ke equation but didnt get it right. I converted everything and divided the diameter by 2. What could I be doing wrong??
 
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Check your moment of inertia for a sphere!
 


There are a few things that could be causing an error in your calculation. First, make sure you are using the correct units for all values. Mass should be in kilograms, diameter in meters, and angular velocity in radians per second. Also, double check that you are using the correct formula for moment of inertia (I = 1/2 * m * r^2) and that you are using the correct value for the radius (in this case, half of the diameter). It's possible that you may have made a small error in your calculations or used the wrong values. I would recommend double checking your work and if you're still having trouble, try approaching the problem from a different angle or asking for help from a classmate or teacher.
 

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