Rotational energy problems

When you try to solve problems of Physics in general and of work and energy in particular, it is important to follow a certain order. Try to be organized when you solve these problems, and you will see how it gives good results. It is worth spending a bit of time on the analysis of a problem before tackling it.

  • Read carefully the problem statement
  • Draw a picture of the physical situation described in the problem.
  • Write in your notebook the givens in the problem statement.
  • The first thing that you must analyze when you are going to solve a rotational energy problem is if the mechanical energy (kinetic + potential) is conserved or not in the situation that arises in the problem.

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The basic equation that you will have to learn to manage to solve this type of problems is the following:

Where EC is the kinetic energy of the solid and W the work (with its sign) of each of the forces acting on it. Keep in mind that a solid can have a rotational energy (if it is rotating), a translation kinetic energy (if its center of mass is displaced) or both.

Then, depending on whether the forces are conservative or not, the work that appears in the second member can be written in terms of the variation of the potential energy of the mass center of the solid.

When a solid rolls without slipping, it experiences a friction force that does not produce work. As a result its mechanical energy is conserved (the work of the friction force is zero) and we can use the relation between the speed of the center of mass, the radius and the angular velocity :

This condition will allow you to eliminate an unknown quantity in the equation resulting from applying conservation of energy.

  • You must choose an origin of heights to calculate the gravitational potential energy. For a solid body, use the height of its center of mass with respect to that origin.
  • Do not forget to include the units in your results.
  • Review the problem and check that the results you have obtained make sense.

On the following pages you will find solved problems of rotational energy. Try to do them before looking at the solution.

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