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The linear velocity of a body rotating at ω rad/s along a circular path of radius r is given by
- a)ω.r
- b)ω/r
- c)ωs2.r
- d)ωs2/r
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The linear velocity of a body rotating at ω rad/s along a circul...
A given angular velocity depends on the distance from the axis of rotation. This relationship is described by the formula:
v = r x ω
where:
v = linear velocity
r = distance from the axis of rotation
ω = angular velocity
This formula applies to any object rotating around an axis, such as a wheel, a spinning top, or the Earth. The linear velocity is directly proportional to the distance from the axis of rotation, which means that the farther away an object is from the axis, the faster it moves.
For example, consider a wheel with a radius of 0.5 meters that is rotating at a rate of 10 revolutions per second. The angular velocity of the wheel is:
ω = 10 x 2π = 62.83 radians per second
Using the formula above, we can calculate the linear velocity of a point on the edge of the wheel:
v = 0.5 x 62.83 = 31.42 meters per second
This means that a point on the edge of the wheel is moving at a speed of 31.42 meters per second, or approximately 112.5 kilometers per hour. Note that the linear velocity is highest at the edge of the wheel, where the distance from the axis is greatest.
v = r x ω
where:
v = linear velocity
r = distance from the axis of rotation
ω = angular velocity
This formula applies to any object rotating around an axis, such as a wheel, a spinning top, or the Earth. The linear velocity is directly proportional to the distance from the axis of rotation, which means that the farther away an object is from the axis, the faster it moves.
For example, consider a wheel with a radius of 0.5 meters that is rotating at a rate of 10 revolutions per second. The angular velocity of the wheel is:
ω = 10 x 2π = 62.83 radians per second
Using the formula above, we can calculate the linear velocity of a point on the edge of the wheel:
v = 0.5 x 62.83 = 31.42 meters per second
This means that a point on the edge of the wheel is moving at a speed of 31.42 meters per second, or approximately 112.5 kilometers per hour. Note that the linear velocity is highest at the edge of the wheel, where the distance from the axis is greatest.
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Community Answer
The linear velocity of a body rotating at ω rad/s along a circul...
If the displacement is along a circular path, then the direction of linear velocity at any instant is along the tangent at that point.
therefore, the linear velocity will be ω.r
therefore, the linear velocity will be ω.r
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