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alisha [4.7K]
3 years ago
11

Two formula one racing cars are negotiating a circular turn, and they have the same centripetal acceleration. however, the path

of car a has a radius of 49.6 m, while that of car b is 39.3 m. determine the ratio of the angular speed of car a to the angular speed of car
b.
Physics
1 answer:
lesantik [10]3 years ago
5 0
The centripetal acceleration of a car following a circular path is:
a_c = \omega^2 r
where \omega is the angular speed of the car, and r is the radius of the orbit.

The problem says that the centripetal acceleration of car A is equal to that of car B, so we can write
a_{cA} = a_{cB}
which becomes
\omega_A^2 r_A = \omega_B ^2 r_B
or
\frac{\omega_A}{\omega_B} =  \sqrt{ \frac{r_B}{r_A} }

and by using the radii of the two orbits, r_A = 49.6 m and r_B = 39.3 m, we can find the ratio between the two angular speeds:
\frac{\omega_A}{\omega_B}= \sqrt{ \frac{r_B}{r_A} }=  \sqrt{ \frac{39.3 m}{49.6 m} } =0.89
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