The wheel of radius r rolls without slipping and has an angular velocity w. Writ

Question

The wheel of radius r rolls without slipping and has an angular velocity w. Write an expression for the velocity of point A in terms of theta and show that the velocities of A and B are perpendicular to one another

The correct answer is vA = 2rwsin(theta/s), I just don't know how to find this answer

Explanation / Answer

let translation velocity=v; since it rolls without slipping=>v=r*w; at point A it has two components of velocity; one is translation velocity in horizontal direction and another one rotational in tangential direction; resultant velocity=square root of(v^2+(rw)^2+2*v*rw*cos(180-theta)); since v=rw=> Va=square root(2*(rw)^2(1-cos(theta)); Va=square root(4*(rw)^2*sin^2(theta/2)); Va=2rwsin(theta/2); write Va and Vb in vector form then dot product of Va and Vb gives you zero; so Va and Vb are perpendicular to one another

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