Concept explainers
A wheel moves in the xy plane in such a way that the location of its center is given by the equations xO = 12t3 and yO = R = 2, where xO and yO are measured in feet and t is measured in seconds. The angular displacement of a radial line measured from a vertical reference line is θ = 8t4, where θ is measured in radians. Determine the velocity of point P located on the horizontal diameter of the wheel at t = 1 s.
Fig. P15.248
Find the velocity of the point P located on the horizontal diameter at time
Answer to Problem 15.248RP
The velocity of the point P located on the horizontal diameter at time
Explanation of Solution
Given information:
Show the location of the center of the wheel as follows:
Here,
The angular displacement of the radial line measured from vertical reference line is denoted by
Show the angular displacement
Here,
Calculation:
Consider the position of the point P with respect to point O is denoted by
Calculate the angular velocity of the wheel at time
Substitute
Substitute
Calculate the velocity at point O using the relation:
Substitute
Substitute
Show the relation between the velocity at point P and O as follows:
Substitute
Thus, the velocity of the point P located on the horizontal diameter at time
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Chapter 15 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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