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An object is traveling around a circle with a radius of 10 cm. If in 20 seconds a central angle of 1/3 radian is swept out, what is the linear speed of the object?

Verified Answer :

arthurpdc

Firstly, we will find the distance covered by the object in the 20 seconds:

\(\text{angle}(in~radians)=\dfrac{\text{arch}}{\text{radius}}\Longrightarrow \dfrac{1}{3}=\dfrac{d}{10~cm}\iff d=\dfrac{10}{3}~cm\)

We must know that \(v=\dfrac{d}{\Delta t}\). So:

\(v=\dfrac{d}{\Delta t}\Longrightarrow v=\dfrac{\dfrac{10}{3}~cm}{20~s}\iff \boxed{v=\dfrac{1}{6}~cm/s}\)

fichoh

The linear speed of the object is \(\frac{1}{6}\)

  • The Radius, r = 10 cm
  • The Fraction of Radius swept out = \(\frac{1}{3}\)
  • The distance = \(10 \div \frac{1}{3}\)
  • The distance covered = \(\frac{10}{3}\)

The linear speed :

  • Radius swept out ÷ time taken
  • \(\frac{10}{3} \times \frac{1}{20} = \frac{1}{6}\)

The linear speed of the object is \(\frac{1}{6}\)

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