Angular velocity describes the rate at which an object is rotating about an axis. It quantifies how fast an object’s angular position is changing with time. Angular velocity is a vector quantity; hence, it has a magnitude and a direction. The magnitude describes the rate of rotation, and the direction describes the axis around which the rotation occurs. The MDCAT exam needs understanding of this concept to solve problems of rotational motion and dynamics related to rotating objects.
Formula for Angular Velocity
The angular velocity (
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ω is defined to be the time derivative of angular displacement:
ℬ
=
Δ
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Δ
????
ω=
Δt
Δθ
where:
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ω is the angular velocity,
Δ
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Δθ is the change in angular displacement (in radians),
Δ
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Δt is the time interval.
For an object moving in uniform circular motion, its angular velocity is constant, and it can also be related to the number of revolutions per second (frequency,
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f) by the formula:
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=
2
????
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ω=2πf
where
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f is the frequency in revolutions per second (Hz). The angular velocity is normally given in radians per second (rad/s). MDCAT students should know how to find the angular velocity in both situations: from angular displacement, and from frequency.
MDCAT Quiz: Angular Velocity Questions
In the MDCAT Quiz, there may be questions that require the student to find angular velocity when the angular displacement and time interval are given, or when frequency is given. For example, a question might ask for the angular velocity of a wheel rotating at a certain rate or how long it takes for an object to complete a certain number of revolutions. Students may also be asked to convert between angular velocity in radians per second and linear velocity, which is related to angular velocity by the formula:
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=
????
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v=ωr
where
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v is the linear velocity,
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R is the radius of the circular path and
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ω represents the angular velocity. The solution to these problems is based on a good understanding of the relationship between angular quantities and their linear counterparts, and being able to apply the appropriate formulae.
Free Flashcards for Angular Velocity
Free flashcards on angular velocity will help MDCAT students. They may include key formulas for angular velocity, examples of solving angular velocity, and practice questions concerning uniform and non-uniform rotational motion. Regular review of these flashcards will make students comfortable with angular velocity and increase their ability to solve rotational motion problems both accurately and rapidly during the MDCAT Quiz. Flashcards are an effective study tool for mastering angular motion concepts and ensuring success on the exam.
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