Concept explainers
Knowing that the disk has a constant angular velocity of 15 rad/s clockwise, determine the angular velocity of bar BD and the velocity of collar D when (a) θ = 0, (b) θ = 90°, (c) θ = 180°.
Fig. P15.57 and P15.58
(a)
Find the angular velocity of the bar BD and velocity of the collar D when
Answer to Problem 15.57P
The the angular velocity of the bar BD and velocity of the collar D when
Explanation of Solution
Given information:
The constant angular velocity of the disk is
The distance AB is
Calculation:
Show the disk as shown in Figure 1.
Refer to Figure 1.
Calculate the velocity at B using the relation:
Substitute
Consider that
Show the velocity
Calculate the value of angle
Consider bar BD.
Show the velocity diagram as shown in Figure 2.
Refer to Figure 2.
Show the relation between the velocity
Calculate the velocity of point D with respect to B using the relation:
Substitute
Calculate the angular velocity of bar BD using the relation:
Substitute
Thus, the angular velocity of bar BD is
Calculate the velocity of the collar
Substitute
Thus, the velocity of the collar D is
(b)
Find the angular velocity of the bar BD and velocity of the collar D when
Answer to Problem 15.57P
The angular velocity of the bar BD and velocity of the collar D are
Explanation of Solution
Calculation:
Refer to Part (a).
Show the disk as shown in Figure 3.
Refer Figure 3.
Calculate the velocity at B using the relation:
Substitute
Consider
Show the velocity
Calculate the value of angle
Consider bar BD.
Show the relation between the velocity
Equate the horizontal component of Equation (1).
Equate the vertical component of Equation (1).
Substitute 0 for
Thus, the velocity of the collar is
Calculate the angular velocity of bar BD using the relation:
Substitute
Thus, the angular velocity of bar BD is
(c)
Find the angular velocity of the bar BD and velocity of the collar D when
Answer to Problem 15.57P
The angular velocity of the bar BD and velocity of the collar D when
Explanation of Solution
Given information:
The constant angular velocity of the disk is
The distance AB is
Calculation:
Show the disk as shown in Figure 4.
Refer Figure 4.
Calculate the velocity at B using the relation:
Substitute
Consider
Show the velocity
Calculate the value of angle
Consider bar BD.
Show the velocity diagram as shown in Figure 5.
Refer Figure 5.
Show the relation between the velocity
Calculate the velocity of point D with respect to B using the relation:
Substitute
Calculate the angular velocity of bar BD using the relation:
Substitute
Thus, the angular velocity of bar BD is
Calculate the velocity of the collar
Substitute
Thus, the velocity of the collar D is
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Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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