Answer:
vâ / vâ = 1.2
Explanation:
- By definition the angular velocity is the rate of change of the angle traveled respect from time, as follows:
    [tex]\omega = \frac{\Delta \theta}{\Delta t} (1)[/tex]
- Now by definition of angle, we can replace in (1) Îθ, by the following expression:
    [tex]\Delta \theta = \frac{\Delta s}{r} (2)[/tex]
- Replacing (2) in (3) Â we have, since :
- [tex]\omega = \frac{\Delta s}{\Delta t*r} (3)[/tex]
- Now, by definition of linear velocity, we know that Îs/Ît = v.
- Replacing in (3), we have a fixed relationship between angular and linear velocity, as follows:
    [tex]\omega =\frac{v}{r} (4)[/tex]
- Now, since we know that the angular velocity for both motorcycles is the same, if we call râ to the smaller radius (15 m), we can write the following proportion:
    [tex]\frac{v_{1} }{r_{1} } = \frac{v_{2}}{r_{2}} (5)[/tex]
- Rearranging terms, and replacing by the values of the radii, we have:
    [tex]\frac{v_{2} }{v_{1}} =\frac{r_{2} }{r_{1} } =\frac{18 m}{15 m} = 1.2[/tex]
- The ratio of their linear speeds, v2/v1, is just the relationship of their radii, i.e., 1.2.
