Concept explainers
(a)
The acceleration of end B of the rod if
(a)
Answer to Problem 15.244P
The acceleration of end B is
Explanation of Solution
Given information:
The side length of the square plate is
The shaft rotates with a constant angular velocity as
The constant angular velocity with respect to the plate is
Calculation:
Calculate the position of A with respect to O
Calculate the position of B with respect to O
Calculate the rate of rotation of the frame
Calculate the motion relative to the frame
For
Sketch the Free Body Diagram of the plate, the rod AB is located at an angle
Refer to Figure 1.
Calculate the position of B with respect to A
Calculate the position of B with respect to O
Substitute
Calculate the velocity at the point
Substitute
Calculate the velocity at the point B with respect to the frame
Substitute
Calculate the acceleration at the point
Substitute
Calculate the acceleration at B with respect to the frame
Substitute
Calculate the Coriolis acceleration
Substitute
Calculate the acceleration at B
Substitute
Hence, the acceleration of B is
(b)
The acceleration of end B of the rod if
(b)
Answer to Problem 15.244P
The acceleration of end B is
Explanation of Solution
Given information:
The side length of the square plate is
The shaft rotates with a constant angular velocity as
The constant angular velocity with respect to the plate is
Calculation:
For
Sketch the Free Body Diagram of the plate, the rod AB is located at an angle
Refer to Figure 2.
Calculate the position of B with respect to A
Calculate the position of B with respect to O
Substitute
Calculate the velocity at the point
Substitute
Calculate the velocity at the point B with respect to the frame
Substitute
Calculate the acceleration at the point
Substitute
Calculate the acceleration at B with respect to the frame
Substitute
Calculate the Coriolis acceleration
Substitute
Calculate the acceleration at B
Substitute
Hence, the acceleration of B is
(c)
The acceleration of end B of the rod if
(c)
Answer to Problem 15.244P
The acceleration of end B is
Explanation of Solution
Given information:
The side of the square plate of side
The shaft rotates with a constant angular velocity
The constant angular velocity with respect to the plate is
Calculation:
For
Sketch the Free Body Diagram of the plate, the rod AB is located at an angle
Refer to Figure 3.
Calculate the position of B with respect to A
Calculate the position of B with respect to O
Substitute
Calculate the velocity at the point
Substitute
Calculate the velocity at the point B with respect to the frame
Substitute
Calculate the acceleration at the point
Substitute
Calculate the acceleration at B with respect to the frame
Substitute
Calculate the Coriolis acceleration
Substitute
Calculate the acceleration at B
Substitute
Hence, the acceleration of B is
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Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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