Answered: A disk with velocity v= 10m/s, mass m=5…

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A disk with velocity v= 10m/s, mass m=5 kg, and radius r=2 m. Find the total kinetic energy.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 46P

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Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

A disk with velocity v= 10m/s, mass m=5 kg, and radius r=2 m. Find the total kinetic energy.

Expert Solution

Step 1

We know that for a disc:

Inertia(I) is as below.

value of the rotational kinetic energy is:

value of the translational kinetic energy is:

Step 2

So, total kinetic energy(E_T) is given as below.

hence putting values above will give us the final total kinetic energy expression:

so, we have:

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