The wheel of Q. 6, shown again here, rolls to the right without slipping, with its center O having a velocity v O = 3m/s. Locate the instantaneous center of zero velocity and use it to find the velocity of point A for the position indicated.
Text Solution
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Sol. The point on the rim of the wheel in contact with the ground has no velocity if the wheel is not slipping; it is, therefore, the instantaneous center C of zero velocity. The angular velocity of the wheel becomes
[ ω = v/r] w = 
= 3/0.300 = 10 rad/s
The distance from A to C is
= 
= 0.436m
The velocity of A becomes
[v = r ω ] v A = 
= 0.436(10) = 4.36 m/s
The direction of v A is perpendicular to AC as shown.
Helpful Hints:
(i) Be sure to recognize that the cosine of 120º is itself negative.
(ii) From the results of this problem, you should be able to visualize and sketch the velocities of all points on the wheel.
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