Question about rotational energy.

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SUMMARY

The discussion focuses on ranking five objects by their rotational energy, utilizing the formula E = (1/2)Iw². The objects include a solid sphere, thin rod, solid cylinder, thin spherical shell, and thin cylindrical shell, each with specified dimensions and angular velocities. The key to solving the problem lies in calculating the moments of inertia for each object, which can be found in standard physics textbooks. Since all objects have equal mass, their rotational energies can be compared directly based on their moments of inertia and angular velocities.

PREREQUISITES
  • Understanding of rotational dynamics and energy
  • Familiarity with the moment of inertia for various shapes
  • Knowledge of angular velocity and its units
  • Ability to apply the formula E = (1/2)Iw²
NEXT STEPS
  • Research the moments of inertia for common shapes, including spheres, rods, and cylinders
  • Study the relationship between angular velocity and rotational energy
  • Explore examples of rotational energy calculations in physics problems
  • Learn about the conservation of angular momentum and its applications
USEFUL FOR

Students studying physics, particularly those focusing on rotational dynamics, as well as educators seeking to enhance their teaching of energy concepts in mechanics.

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Homework Statement


Five objects of equal mass are shown below together with the axis about which they are rotating. Select the objects in order of increasing rotational energy

Solid Sphere, about any diameter, with R = 3 m and ω=5 rad/s


Thin rod, about axis through center, perpendicular to the length with l = 8 m and ω=6 rad/s


Solid Cylinder, about cylinder axis with R = 3 m and ω=5 rad/s


Thin Spherical shell, about any diameter, with R = 2 m and ω=7 rad/s


Thin cylindrical shell, about cylinder axis with R = 1 m and ω=7 rad/s



Homework Equations



(1/2)Iw^2

The Attempt at a Solution



Most of these have no mass or moment of intertia included and I am not sure how to deal with that.
 
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You are supposed to calculate the moments of inertia first. Your textbook must have a table where these are listed. Note that all the masses are the same, therefore you can rank the energies because they will always be

E = (some number)*m
 

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