- #1

bolzano95

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- Homework Statement
- A body is circulating on a fixed circumference with radius R=1m. It moves with an angular velocity ##ω = \frac {k} {\sqrt{φ}}##.

- Relevant Equations
- Relevant equations are listed below in solving process.

What is the angle between acceleration and velocity after 1spin (2π radians)?

First I decided to find out what is the angular acceleration:

##α = \frac {dω} {dt} = \frac {dω} {dt} \frac {dφ} {dφ} = \frac {dω} {dφ} ω \implies ##after integrating ##\implies α = - \frac {k^2} {2φ^2}##

## a_t= αR = - \frac {k^2} {2φ^2} R##

## a_r= ω^2R= \frac {k^2} {φ} R##

## a= \sqrt{a_t^2+a_r^2}=...##

Because ##\vec{v}## is parallel to ##\vec{a_t}## we can use ## tanθ = |\frac {a_r} {a_t}|\implies## after evaluating for ##φ=2π \implies θ=85,45°##

Is this correct?

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