Concept explainers
A square plate of side 2r is welded to a vertical shaft that rotates with a constant angular velocity
Fig. P15.244
(a)
Acceleration of end B if
Answer to Problem 15.244P
The acceleration
Explanation of Solution
Given information:
Constant angular velocity of vertical shaft is
The relative angular velocity of rod AB with respect to the plate is
The acceleration in a three-dimensional motion of a particle relative to rotating frame is defined as:
In the above equation,
The Coriolis acceleration is defined as
Calculation:
Angular velocity
The relative angular velocity
The relative position vector
The relative position vector
Assume
The acceleration
The relative acceleration
At
The relative position vector
The relative position vector
Therefore,
The relative velocity
The relative acceleration
The Coriolis acceleration
Acceleration
Conclusion:
The acceleration
(b)
Acceleration of end B if
Answer to Problem 15.244P
The acceleration
Explanation of Solution
Given information:
Constant angular velocity of vertical shaft is
The relative angular velocity of rod AB with respect to the plate is
The acceleration in a three dimensional motion of a particle relative to rotating frame is defined as:
In the above equation,
The Coriolis acceleration is defined as
Calculation:
At
The relative position vector
The relative position vector
Therefore,
The relative velocity
The relative acceleration
The Coriolis acceleration
Acceleration
Conclusion:
The acceleration
(c)
Acceleration of end B if
Answer to Problem 15.244P
The acceleration
Explanation of Solution
Given information:
Constant angular velocity of vertical shaft is
The relative angular velocity of rod AB with respect to the plate is
The acceleration in a three dimensional motion of a particle relative to rotating frame is defined as:
In the above equation,
The Coriolis acceleration is defined as
Calculation:
At
The relative position vector
The relative position vector
Therefore,
The relative velocity
The relative acceleration
The Coriolis acceleration
Acceleration
Conclusion:
The acceleration
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