12 Questions
What does 𝜔 ⃗ × (𝜔 ⃗ × 𝑟) represent?
Centripetal acceleration in the starred frame
When does the Coriolis acceleration term appear?
When the particle is moving with a velocity in the starred system
What does the term 𝑣) ⃗⃗⃗ 𝑑∗ 𝜔 𝑑𝑡 × 𝑟 represent?
Azimuthal acceleration
What force is represented by 𝐹.⃗⃗⃗⃗?
Real force
What is the magnitude of the angular velocity 𝜔 ⃗?
𝜔 = |𝜔 ⃗ | = 𝑑𝑡
What does equ(17) give the time derivative of?
A vector fixed in the starred frame
In which direction is the magnitude | 𝑑𝑅⃗ /𝑑𝑡 |?
Tangential to the curve at P
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
What is the equation for the motion of a particle in the starred frame?
𝑟⃗⃗ = 𝑟⃗⃗⃗∗ +𝑅⃗
What does 𝑚𝑎 ⃗⃗⃗⃗⃗∗ represent in the context of the given text?
Force in the starred frame
What does an unaccelerated frame (O*) moving with constant velocity relative to O imply?
𝑎𝑅 = 0 and ⃗⃗⃗⃗ ⃗⃗⃗⃗∗ = 𝐹
What are frames of reference in which Newton’s equations of motion are valid called?
Inertial frames
Test your understanding of differentiating vectors with respect to time using the given equations and derivations. Explore the relationship between velocity, acceleration, and Newton's equations in both starred and unstarred frames.
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