PHY 2121/2521 ASSIGNMENT 2 OF 2022
DUE DATE:06 MAY 2022
1.
A primed coordinate system rotates about the 𝑧-axis with angular velocity
𝜔
⃗ = 𝑖̂′ cos 𝑡 + 𝑗̂′ sin 𝑡 relative to a fixed coordinate system, where 𝑡 is the time.
The origin of the primed system has position vector 𝑅⃗0 = 𝑖̂′ 𝑡 − 𝑗̂′ + 𝑘̂ ′ 𝑡 2 with
respect to the fixed system. The position vector of a particle is given by 𝑟 ′ =
𝑗̂′ 𝑡 + 𝑘̂ ′ relative to the moving system. Calculate the true velocity of the
particle and the acceleration of the moving system.
2.
A particle moving in a central force field located at 𝑟 = 0 describes the spiral
𝑟 = 𝑒 −𝜃 . Show that the force varies as the inverse third power of 𝑟.
3.
Using 𝑟 = 𝑎(1 − cos 𝜃) in the equation
𝑓(𝑟) =
𝑚𝑙 2 𝑑 2 𝑟 2 𝑑𝑟 2
[
− ( ) − 𝑟]
𝑟 4 𝑑𝜃 2 𝑟 𝑑𝜃
show that the force varies as the inverse fourth power of 𝑟.
4.
Show that the position of a particle as a function of time 𝑡 can be determined
from the equation 𝑡 = ∫[𝐺(𝑟)]−1/2 𝑑𝑟, where
𝐺(𝑟) =
2𝐸 2
𝑙2
+ ∫ 𝑓(𝑟) 𝑑𝑟 − 2
𝑚 𝑚
𝑟
END OF ASSIGNMENT