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 the point P located on the horizontal diameter of the wheel at t = 1.4 s.

the velocity of the point P located on the horizontal diameter of the wheel at t = 1.4 s  is  

Explanation:

The free-body  diagram below shows the interpretation of the question; from the diagram , the wheel that is rolling in a clockwise directio will have two velocities at point P;

Now;

Also,

where (angular velocity) =

∴ the velocity of the point P located on the horizontal diameter of the wheel at t = 1.4 s  is  

since you're a real machine, your ama is always less than your ima, because you can never totally eliminate friction.