Vector Differentiation Quiz
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Questions and Answers

What does 𝜔 ⃗ × (𝜔 ⃗ × 𝑟) represent?

  • Coriolis acceleration in the starred frame
  • Centripetal acceleration in the unstarred frame
  • Azimuthal acceleration in the unstarred frame
  • Centripetal acceleration in the starred frame (correct)

When does the Coriolis acceleration term appear?

  • When the particle is moving with a velocity in the starred system (correct)
  • When the unstarred system is rotating uniformly
  • When the starred system is rotating uniformly
  • When the particle is at rest in the starred system

What does the term 𝑣) ⃗⃗⃗ 𝑑∗ 𝜔 𝑑𝑡 × 𝑟 represent?

  • Tangential acceleration
  • Azimuthal acceleration (correct)
  • Centripetal acceleration
  • Coriolis acceleration

What force is represented by 𝐹.⃗⃗⃗⃗?

<p>Real force (B)</p> Signup and view all the answers

What is the magnitude of the angular velocity 𝜔 ⃗?

<p>𝜔 = |𝜔 ⃗ | = 𝑑𝑡 (B)</p> Signup and view all the answers

What does equ(17) give the time derivative of?

<p>A vector fixed in the starred frame (B)</p> Signup and view all the answers

In which direction is the magnitude | 𝑑𝑅⃗ /𝑑𝑡 |?

<p>Tangential to the curve at P (C)</p> Signup and view all the answers

Why do we not write the right-hand side of equ(17) as 𝑅⃗ × 𝜔 ⃗?

<p>Because the direction of φ is from the axis of rotation (D)</p> Signup and view all the answers

What is the equation for the motion of a particle in the starred frame?

<p>𝑟⃗⃗ = 𝑟⃗⃗⃗∗ +𝑅⃗ (A)</p> Signup and view all the answers

What does 𝑚𝑎 ⃗⃗⃗⃗⃗∗ represent in the context of the given text?

<p>Force in the starred frame (A)</p> Signup and view all the answers

What does an unaccelerated frame (O*) moving with constant velocity relative to O imply?

<p>𝑎𝑅 = 0 and ⃗⃗⃗⃗ ⃗⃗⃗⃗∗ = 𝐹 (D)</p> Signup and view all the answers

What are frames of reference in which Newton’s equations of motion are valid called?

<p>Inertial frames (A)</p> Signup and view all the answers

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