Eduprobe
Question:
The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed ω and (ii) an inner disc of radius 2R rotating anticlockwise with angular speed ω/2. The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30° with the horizontal. Then with respect to the horizontal surface, what is the linear velocity of point P?
the point P has a linear velocity (3−√3/4)Rω^i +1/4Rω^k
the point O has a linear velocity 3Rω^i.
the point P has a linear velocity 11/4Rω^i + √3/4Rω^k
the point P has a linear velocity 13/4Rω^i − √3/4Rω^k.
Solution:
as shown in the diagram
V₀ = (3R)ω^i = 0
therefore V₀ = 3Rω^i
Vₚ,₀ = -Rω/4^i + Rω√3/4^k
Now, Vₚ = Vₚ,₀ + V₀ = 11Rω/4^i + Rω√3/4^k