Concept explainers
Two disks, each of 130-mm radius, are welded to the 500-mm rod CD. The rod-and-disks unit rotates at the constant rate
Fig.P15.254
(a)
Velocity and acceleration of point E
Answer to Problem 15.245P
The velocity
The acceleration
Explanation of Solution
Given information:
The relative angular velocity of disk and rod with respect to arm AB is
The angular velocity of arm AB is
The velocity in a three dimensional motion of a particle relative to rotating frame is defined as:
In the above equation,
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:
The relative position vector
The relative position vector
Assume Bxyz as the rotating frame of reference.
The constant angular velocity
The relative angular velocity
Assume
The velocity
The relative velocity
The velocity
The acceleration
The relative acceleration
The Coriolis acceleration
The acceleration
Conclusion:
The velocity
The acceleration
(b)
Velocity and acceleration of point F
Answer to Problem 15.245P
The velocity
The acceleration
Explanation of Solution
Given information:
The relative angular velocity of disk and rod with respect to arm AB is
The angular velocity of arm AB is
The velocity in a three dimensional motion of a particle relative to rotating frame is defined as:
In the above equation,
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:
The relative position vector
The relative position vector
Assume Bxyz as the rotating frame of reference.
The constant angular velocity
The relative angular velocity
Assume
The velocity
The relative velocity
The velocity
The acceleration
The relative acceleration
The Coriolis acceleration
The acceleration
Conclusion:
The velocity
The acceleration
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Chapter 15 Solutions
Vector Mechanics For Engineers
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