Concept explainers
The disk shown moves in the xy plane. Knowing that (vA)y = −7 m/s, (vB)x = −7.4 m/s, and (vC)x = −1.4 m/s, detemine (a) the velocity of point O, (b) the point of the disk with zero velocity.
Fig. P15.44 and P15.45
(a)
![Check Mark](/static/check-mark.png)
Find the angular velocity of point O.
Answer to Problem 15.45P
The angular velocity of point O is
Explanation of Solution
Given information:
Show the velocity
Consider the velocity of point C and B with respect to A is denoted by
Consider the position of point C, B, O with respect to A is denoted by
Calculation:
Show the position
Calculate the velocity
Substitute
Show the components of i on both sides of the Equation (1).
Show the components of j on both sides of the Equation (1).
Calculate the velocity
Substitute
Show the components of the i on both sides of the Equation (4).
Show the components of the j on both sides of the Equation (4).
Refer Equation (2).
Substitute
Calculate the velocity
Substitute
Consider the velocity at the point O is denoted by
Consider the velocity of the point O with respect to A is denoted by
Calculate the velocity of the point O using the relation:
Substitute
Thus, the velocity of the point O is
(b)
![Check Mark](/static/check-mark.png)
Find the point in the disk with zero velocity.
Answer to Problem 15.45P
The point on the disk with zero velocity is
Explanation of Solution
Given information:
Calculation:
Consider the point on the disk with zero velocity is
Show the distance
The velocity
Show the velocity
Substitute 0 for
Equate i component on both sides of the Equation (7).
Equate j component on both sides of the Equation (7).
Thus, the point with zero velocity is
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Chapter 15 Solutions
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