Question

the center of a disk rolling without slipping on a plane surface moves with speed u a particle on the lower half of the rim making an angle 60 degree with vertical will be moving at speed

Answer 1

Since the situation is that of a velocity of any point on the wheel will be the same.

let the angular velocity =w

since the wheel is rolling, w=v/R

where v=velocity of centre of wheel and R is the radius.

Now let any point on the wheel be considered at a radius of r.

Its tangential velocity =u=r.w

Putting w as v/R

u=r.v/R

This 'u' is its tangential velocity.

By knowing the angle between the tangential velocity of centre, use vector addition to obtain the net resultant velocity of that point.