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)
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)
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
<LCPO> VECTOR MECH,STAT+DYNAMICS
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