A wheel with a 1 foot radius spins in place in a counterclockwise direction. Explain why the distance point P travels is the same as the angle of revolution (measured in radians) of this wheel?

A radian is a unit of angle measurement such that a central angle of a circle measuring 1 radian subtends and arc of the circle whose length equals the radius if the circle.

In this case, the radius is 1 foot. Point P travels along the arc formed by an angle. When the angle is 1 radian, the arc length equals the radius of the circle, 1 foot. It is simply following the definition of radian.

ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-04-26T13:13:38+02:00

Point P will travel a 2π distance in a complete revolution i.e. the distance point P travels is the same as the angle of revolution.

What is 1 radian?

One radian is defined as the angle subtended from the centre of a circle which intercepts an arc equal in length to the radius of the circle.

Circumference of the circle = 2π(1) =2π feet.

This means point P will travel a 2π distance in a complete revolution.

A complete revolution = 360° or 2π

Hence, point P will travel a 2π distance in a complete revolution i.e. the distance point P travels is the same as the angle of revolution.

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