Question

Find the angular velocity in both rad/s and m/s. Here is the info we have:

Distance: 11.5 inches
Radius: 5 centimeters
Diameter: 10 centimeters
Mass: 500 mL

a) 6.61 rad/s, 0.165 m/s
b) 1.85 rad/s, 0.056 m/s
c) 4.42 rad/s, 0.1105 m/s
d) 3.14 rad/s, 0.0785 m/s

Answer 1

The angular velocity can be calculated using the formula angular velocity = linear velocity / radius. Convert the given distance and radius to the same unit, and then use the formula to calculate the angular velocity.

Step-by-step explanation:

The angular velocity can be calculated using the formula angular velocity = linear velocity / radius. Since the distance is given in inches and the radius is given in centimeters, we need to convert them to the same unit before calculating.

First, let's convert the distance from inches to meters. 1 inch is equal to 0.0254 meters. So, the distance in meters is 11.5 inches * 0.0254 meters/inch = 0.2921 meters.

Next, let's convert the radius from centimeters to meters. 1 centimeter is equal to 0.01 meters. So, the radius in meters is 5 centimeters * 0.01 meters/centimeter = 0.05 meters.

Using the formula, angular velocity = linear velocity / radius, we can calculate the angular velocity in rad/s. The linear velocity is given in m/s, so we don't need to convert it. Substitute the values into the formula:

angular velocity = 0.165 m/s / 0.05 meters = 3.3 rad/s.

So, the correct answer is (d) 3.3 rad/s.