(a)
The percent of total kinetic energy of a sphere is its translational kinetic energy.
(a)
Answer to Problem 84P
Explanation of Solution
Given:
A uniform sphere is rolling without friction.
Formula used:
The total kinetic energy is sum of translational kinetic energy and rotational kinetic energy is given as:
Where, m is the mass, v is the velocity, I is the moment of inertia and
Calculation:
Translational Kinetic energy of sphere
Kinetic energy of an object is the sum of its rotational kinetic energy and translational kinetic energy which can be determined as follows
The ratio of translational kinetic energy and rotational kinetic energy is given as
For sphere,
Therefore,
Conclusion:
71.4% percentage of a sphere total kinetic energy is its translational kinetic energy
(b)
The percent of kinetic energy is translational kinetic energy of a uniform cylinder.
(b)
Answer to Problem 84P
66.7%
Explanation of Solution
Given:
Uniform Cylinder is rolling without friction.
Formula used:
The total kinetic energy is sum of translational kinetic energy and rotational kinetic energy is given as:
Where, m is the mass, v is the velocity, I is the moment of inertia and
Calculation:
Translational Kinetic energy of uniform cylinder
Kinetic energy of an object is the sum of its rotational kinetic energy and translational kinetic energy which can be determined as follows
The ratio of translational kinetic energy and rotational kinetic energy is given as
For uniform cylinder
Therefore,
Conclusion:
66.7% percentage of a uniform cylinder total kinetic energy is its translational kinetic energy
(c)
The percent of total kinetic energy of a hoop is its translational kinetic energy.
(c)
Answer to Problem 84P
50%
Explanation of Solution
Given:
Hoop is rolling without friction
Formula used:
The total kinetic energy is sum of translational kinetic energy and rotational kinetic energy is given as:
Where, m is the mass, v is the velocity, I is the moment of inertia and
Calculation:
Translational Kinetic energy of a hoop
Kinetic energy of an object is the sum of its rotational kinetic energy and translational kinetic energy which can be determined as follows
The ratio of translational kinetic energy and rotational kinetic energy is given as
For hoop
Therefore,
Conclusion:
50.0% percentage of a sphere total kinetic energy is its translational kinetic energy
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Chapter 9 Solutions
Physics for Scientists and Engineers
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