Concept explainers
The plate shown moves in the xy plane. Knowing that
(a)
The angular velocity of the plate.
Answer to Problem 15.46P
The angular velocity of the plate is
Explanation of Solution
Given Information:
The figure below shows a plate moving in x-y plane.
Figure-(1)
The velocity along x- direction of the point A is
Write the expression for position vector of AB.
Here, the coordinates of point A is
Write the expression for the velocity at point A.
Here, the velocity of point A along x -direction is
Write the expression for the velocity at point B.
Here, the velocity of point B along x -direction is
Write the expression for the velocity at point C.
Here, the velocity of point C along x -direction is
Write the expression to calculate the velocity of point B.
Here, the angular velocity of the plate is
Write the expression for velocity at point C.
Write the expression for position vector of CA.
Here, the coordinates of point C is
Calculation:
Substitute
Substitute
Substitute
Substitute
Equate the coefficients of
Conclusion:
The angular velocity of the plate is
(b)
The velocity of point A.
Answer to Problem 15.46P
The velocity of point A is
Explanation of Solution
Write the expression for velocity of point A.
Calculation:
Substitute
Substitute
Equate the coefficients of j in Equation (XII).
Substitute
Conclusion:
The velocity of point A is
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Chapter 15 Solutions
Vector Mechanics for Engineers: Dynamics
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