A wheel of radius r=1 m is rolling with an angular velocity ω=π3 rad/s about its center and velocity of its center of mass is vcom=2 m/s. Point P(0,0) is in contact with ground initially, find its height (in m) from the surface after time t=1 s.
A
0.4
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B
0.3
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C
0.5
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D
0.6
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Solution
The correct option is C0.5
Height of the point will be the displacement in y−axis.
So, analysing only rotational motion about COM,
We know that displacement of point P in y− direction is given as Δy=r−rcosθ
also, θ=ω×t=(π3×1) rad ⇒Δy=1−1×cosπ3Δy=(1−12)^j=0.5^jm ∴ Height of point P after 1s=0.5m