Solved problem: Position vector in u.c.m.

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Statement

difficulty

A body describes a uniform circular motion with a 3 m radius. What is its position vector when its angle is 30º?

Solution

Data

R = 3 m
φ = 30º = 1/6 π rad

Resolution

Knowing that the position vector of a body in a uniform circular motion (u.c.m.) is obtained from the following expression:

\vec{r} = x \cdot \vec{i} + y \cdot \vec{j} = R \cdot \cos (φ) \cdot \vec{i} + R \cdot \sin (φ) \cdot \vec{j}

We only need to substitute the data that we know in this equation:

$\vec{r} = 3 \cdot \cos (\frac{1}{6} \cdot π) \cdot \vec{i} + 3 \cdot \sin (\frac{1}{6} \cdot π) \cdot \vec{j} \Rightarrow \vec{r} = 2.6 \cdot \vec{i} + 1.5 \cdot \vec{j}$

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas

Related sections

\vec{r} = x \cdot \vec{i} + y \cdot \vec{j} = R \cdot \cos (φ) \cdot \vec{i} + R \cdot \sin (φ) \cdot \vec{j}

Uniform Circular Motion (U.C.M.)

Non-Uniform Circular Motion

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Solution

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Position vector in u.c.m.

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Solution

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