Question

an amusement park ride has cars that move around a circular track at the rate of 16 revolutions in 20 seconds. to the nearest hundredth, the angular velocity of the cars is radians per second.

Explanation:

Step1: Calculate the total angle in radians

One revolution is \(2\pi\) radians. For \(16\) revolutions, the total angle \(\theta=16\times2\pi = 32\pi\) radians.

Step2: Use the angular velocity formula

The formula for angular velocity \(\omega=\frac{\theta}{t}\), where \(\theta\) is the angle in radians and \(t\) is the time in seconds. Given \(t = 20\) seconds and \(\theta=32\pi\) radians. Then \(\omega=\frac{32\pi}{20}\).

Step3: Simplify the expression

\(\omega=\frac{8\pi}{5}\approx\frac{8\times3.14159}{5}=\frac{25.13272}{5}=5.026544\approx5.03\) radians per second.

Answer:

$5.03$