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The angular velocity of an object is 10 rad/s. find the linear velocity of the object, if the radius of circle in which the object is moving is 10m.

The angular velocity of an object is 10 rad/s. find the linear velocity of the object, if the radius of circle in which the object is moving is 10m. Correct Answer 100 m/s

The correct answer is option 3) i.e. 100 m/s.

CONCEPT:

  • Angular velocity: The rate of change of angular position of an object in a rotational/circular motion is called angular velocity.
    • The SI unit of angular velocity is radian per second.

It is given by the formula:

ω = dθ/dt

where, ω = angular velocity in radian per second, θ = angular displacement in radian, and t = time in second.

EXPLANATION:

  • Relation of angular velocity with linear velocity: The relation between the angular velocity of an object and its linear velocity is

V = ω × r

where, V = linear velocity of the object in metre per second, ω = angular velocity of the object in radian per second, and r = radius of the circle in which the body is moving in metre.

CALCULATION:

Given data,

angular velocity, ω = 10 rad/s

radius of the circle, r = 10m

We know that,

V = ω × r

putting the respective values in the above equation we get,

V = 10 × 10 m/s

⇒ V = 100 m/s.

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