Name Surname:
Number:
FIZ-284E QUIZ 1
̂ , where the coordinates 𝒙,
1) A vector ⃗𝑨 is given in Cartezian coordinates as ⃗𝑨 = 𝒛𝚤̂ − 𝟐𝒙 𝒋̂ + 𝟑𝒚 𝒌
𝒚, and 𝒛 are time dependent.
⃗⃗ in cylindrical coordinates where 𝑥 = ρ cos 𝜙, 𝑦 = ρ sin 𝜙 and 𝑧 = 𝑧. What are
(a) Obtain the vector 𝑨
the components 𝐴𝜌 , 𝐴𝜑 and 𝐴𝑧 of the vector ⃗𝑨 in cylindrical coordinates? (2 sin 𝜙 cos 𝜙 = sin 2𝜙)
⃗ ̇ in cylindrical coordinates. (The dot denotes derivative with respect to time 𝑡.)
(b) Obtain the vector ⃗𝑨
⃗⃗ ̇ ? (cos 2𝜙 = cos2 𝜙 − sin2 𝜙)
What are the components 𝐴̇ , 𝐴̇ ve 𝐴̇ of the vector 𝑨
𝜌
Form No: DYS-1a
𝜙
𝑧