A particle moves in a circular path of radius $20 cm$ as shown. Find angular velocity of particle w.r.t an axis passing through centre of the circle and perpendicular to plane of the circle.

10 rad/s

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15 rad/s

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30 rad/s

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40 rad/s

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Solution

The correct option is B $15 rad/s$
We know that relation between speed and angular velocity is,

$ω_{A C} = \frac{(v_{A C})_{⊥}}{A C}$

Given $v_{A} = 3 m / s$ ,
So, $v_{A C} = v_{A} = 3 m / s$

As the radius is $20 cm$ , the distance of $A C$ will be $20 cm = \frac{20}{100} m$

$\Rightarrow ω_{A C} = \frac{3}{20 \times \frac{1}{100}} = 15 rad/s$

Hence option B is the correct answer.

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A particle moves in a circular path of radius 20 cm as shown. Find angular velocity of particle w.r.t an axis passing through centre of the circle and perpendicular to plane of the circle.

The correct option is B 15 rad/sWe know that relation between speed and angular velocity is, ωAC=(vAC)⊥AC Given vA=3 m/s, So, vAC=vA=3 m/s As the radius is 20 cm, the distance of AC will be 20 cm=20100 m ⇒ωAC=320×1100=15 rad/s Hence option B is the correct answer.

A particle moves in a circular path of radius $20 cm$ as shown. Find angular velocity of particle w.r.t an axis passing through centre of the circle and perpendicular to plane of the circle.