Concept explainers
The path of a particle P is a limacon. The motion of the particle is defined by the relations
(a)
The velocity and the acceleration of the particle at
Answer to Problem 11.162P
Velocity of the particle:
Acceleration of the particle:
Explanation of Solution
Given information:
The path of the particle is a limacon.
The motion of the particle is defined by the relation:
Calculations:
From the given relation for the distance of the particle:
Taking the time derivative:
And from another given relation for the angle of the particle:
The time derivatives;
Hence, from the relation for the velocity of particle in polar coordinates:
Now, using the relation for the acceleration of the particle in polar coordinates:
Conclusion:
The velocity of the particle at
(b)
The value of θ for which the magnitude of the velocity is maximum.
Answer to Problem 11.162P
The value of θ :
Explanation of Solution
Given information:
The path of the particle is a limacon.
The motion of the particle is defined by the relation:
Calculations:
The magnitude of the velocity is calculated as:
Conclusion:
The value of θ for which the magnitude of the velocity is maximum is 2np, where,
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Chapter 11 Solutions
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