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A particle is moving with constant speed...

A particle is moving with constant speed in a circle as shown in (Fig. 5.163). Find the angular velocity of the particle A with respect to fixed point `B and C` if angular velocity with respect to `O is omega`.
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Text Solution

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Angular velocity of `A` with respect to `O` is
`omega_(A C) = ((v_(A O))_|_)/(r_(A O)) = (v)/( r)= omega`
`:. omega_(A B) = ((v_(A B))_|_)/(r_(A B))= (v)/(2 r)=(omega)/(2)`
and `omega_(A C) = ((v_(A C))_|_)/(r_(A C)) = (v)/(3 r) = (omega)/(3)`.
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Knowledge Check

  • A particle is moving with constant speed v in xy plane as shown in figure. The magnitude of its angular velocity about point O is

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    `(v)/(b)`
    C
    `(vb)/((a^(2) + b^(2)))`
    D
    `(v)/(a)`

  • A particle is moving with uniform speed 0.5 m//s along a circle of radius 1m then the angular velocity of particle is (in rad s^(-1) )

    A
    `2`
    B
    `1.5`
    C
    `1`
    D
    `0.5`

  • A particle is moving parallel to x-axis as shown in the figure. The angular velocity of the particle about the origin is

    A
    `(v//b)sin^(2)theta`
    B
    `(v//b)`
    C
    `(v//b)sintheta`
    D
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