Concept explainers
The 80-mm-radius wheel shown rolls to the left with a velocity of 900 mm/s. Knowing that the distance AD is 50 mm, determine the velocity of the collar and the angular velocity of rod AB when (a) β = 0, (b) β = 90°.
Fig. P15.71
(a)
Find the velocity of the collar and the angular velocity of rod AB when
Answer to Problem 15.71P
The velocity of the collar and the angular velocity of rod AB when
are
Explanation of Solution
Given information:
The radius of the wheel is
The velocity of the wheel is
Calculation:
Calculate the angular velocity
Substitute
Consider the value of the angle
Consider the position of point A with respect to point D is denoted by
Show the relation between the velocity at A and D as follows:
Substitute
Consider the position of the point B with respect to A is denoted by
Show the relation between the velocity at A and B using the relation:
Substitute
Equate j component of Equation (1) as follows:
Thus, the angular velocity of the rod AB is
Equate i component of Equation (1) as follows:
Substitute 0 for
Thus, the velocity of the collar B is
(b)
Find the velocity of the collar and the angular velocity of rod AB when
Answer to Problem 15.71P
The velocity of the collar and the angular velocity of rod AB when
are
Explanation of Solution
Given information:
The radius of the wheel is
The velocity of the wheel is
Calculation:
Calculate the angular velocity
Substitute
Consider the value of the angle
Consider the position of point A with respect to point D is denoted by
Show the relation between the velocity at A and D as follows:
Substitute
Consider the position of the point B with respect to A is denoted by
Show the relation between the velocity at A and B using the relation:
Substitute
Equate j component of Equation (1) as follows:
Thus, the angular velocity of the rod AB is
Equate i component of Equation (1) as follows:
Substitute
Thus, the velocity of the collar B is
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