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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.⃗⃗⃗⃗?

Real force Signup and view all the answers

What is the magnitude of the angular velocity 𝜔 ⃗?

𝜔 = |𝜔 ⃗ | = 𝑑𝑡 Signup and view all the answers

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

A vector fixed in the starred frame Signup and view all the answers

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

Tangential to the curve at P Signup and view all the answers

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

Because the direction of φ is from the axis of rotation Signup and view all the answers

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

𝑟⃗⃗ = 𝑟⃗⃗⃗∗ +𝑅⃗ Signup and view all the answers

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

Force in the starred frame Signup and view all the answers

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

𝑎𝑅 = 0 and ⃗⃗⃗⃗ ⃗⃗⃗⃗∗ = 𝐹 Signup and view all the answers

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

Inertial frames Signup and view all the answers