an amusement park ride has cars that move around a circular track at the rate of 16 revolutions in 20…

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.

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.

Answer

Answer:

$5.03$

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.