Concept explainers
The 80-kg wheel has a radius of gyration about its mass center O of ko = 400 mm. Determine its angular velocity after it has rotated 20 revolutions starting from rest.
The angular velocity of the wheel after it has rotated 20 revolutions starting from rest.
Answer to Problem 1FP
The angular velocity of the wheel after it has rotated 20 revolutions starting from rest is
Explanation of Solution
Given:
The mass of wheel is
The radius of gyration of wheel about its mass center
The radius of the wheel is
The force acting on the wheel is
Write the formula for mass moment of inertia
Here,
Write the formula for kinetic energy
Here,
Write the formula for work done by the couple moment.
Here,
Write the formula for Principle of Work and Energy.
Here,
Conclusion:
Calculate the mass moment of inertia
Substitute
Calculate the initial and final kinetic energy of the wheel.
At initial:
When the wheel starts from rest.
The initial kinetic energy becomes zero.
At final:
Substitute
Calculate the angular displacement
Calculate the work done by the couple moment
Substitute
Here, the total work done is
Calculate the angular velocity of the wheel after it has rotated 20 revolutions starting from rest.
Substitute
Thus, the angular velocity of the wheel after it has rotated 20 revolutions starting from rest is
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Chapter 18 Solutions
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