A body moves describing a circular trajectory with constant linear and angular velocity equal to 3 m/s and 6π rad/s respectively. Determine its position vector when it has traveled exactly one meter.



ω = 6 π rad/s
v = 3 m/s


If we apply the definitions of the angular magnitudes, we know that:

v=ω·R R = vω R =36π R =0.1 m

Now applying the definition of distance traveled based on the angular position and the radius:

s=φ·R φ=sR φ=10.1φ=10 rad

Now that we know the radius and the angular position when the distance traveled is 1 m, we can determine the position vector using the following expression:

r=R·cos φ · i + R · sin ϕ · j r=0.1·cos 10 rad · i + 0.1 · sin (10 rad) · j r=-0.08 · i - 0.05 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.

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