A wheel is rolling ithout slipping at 487 meters per second to the right on a level surface. the diameter of the wheel is 100 centimeters. What is the angular speed of the wheel in revolutions per minute?

Please walk me through your steps, don't just suggest a formula.
Thank you very much.

n =ω/2•π=v/2•π•R= v/π•D =487/3.14•1=155 rev/s =9300 rev/min.

Are you sure that v=487 m/s? Extremely fast…

I know it IS really fast lol, but that's what is says! Thank you for your help!

To find the angular speed of the wheel in revolutions per minute, we need to first determine the linear speed of a point on the circumference of the wheel, and then convert it to the angular speed.

1. Find the circumference of the wheel:
The circumference of a circle is given by the formula C = π * d, where d is the diameter. In this case, the diameter is 100 centimeters, so the circumference can be calculated as C = π * 100 cm.

2. Convert the linear speed to centimeters per minute:
The linear speed is given as 487 meters per second. To convert this to centimeters per minute, we need to convert meters to centimeters and seconds to minutes.
- There are 100 centimeters in a meter, so the linear speed can be expressed as 487 * 100 centimeters per second.
- There are 60 seconds in a minute, so we further multiply by 60 to get the linear speed in centimeters per minute: (487 * 100) * 60 cm/min.

3. Calculate the angular speed in revolutions per minute:
The angular speed is defined as the linear speed divided by the circumference. So, we divide the linear speed (in cm/min) by the circumference (in cm) to get the angular speed in revolutions per minute:
Angular speed = (487 * 100 * 60) cm/min / (π * 100 cm).

Let's calculate the value:

Step 1: Calculate the circumference of the wheel:
C = π * 100 cm.

Step 2: Convert the linear speed to centimeters per minute:
Linear speed = (487 * 100) * 60 cm/min.

Step 3: Calculate the angular speed in revolutions per minute:
Angular speed = (487 * 100 * 60) cm/min / (π * 100 cm).

Simplifying,
Angular speed = (487 * 100 * 60) / (π * 100) rev/min.

Now you can evaluate this expression to find the value of the angular speed in revolutions per minute.