A car is moving at the rate of 60 miles per hour, and the diameter of its wheels is 2.5 feet (1 mile=5280 feet)

a) Find the angular speed of the wheels in radians per minute
b) Find the number of revolutions per minute the wheels are rotating.

I shouldve known better than to actually think i was gunna get help...

V = linear speed

r = radius

omega = angular velocity

RPM = Revolutions per minute

r = diameter / 2

60 mph = 60 * 5280 ft

V = r * omega

60 * 5280 = ( 2.5 / 2 ) * omega

316,800 = 1.25 omega Divide both sides ba 1,25

316,800 / 1.25 = omega

253,440 = omega

omega = 253,440 radians / h Divide both sides by 60

omega = 253,440/ 60

omega = 4,224 radians / min

1 rotation = 2 pi radians

RPM = 4,224 / 2 pi

RPM = 2112/ pi

RPM = 2112 / 3.1416

RPM = 672.2689 rotation / min

To find the angular speed of the wheels in radians per minute, we first need to convert the linear speed of the car from miles per hour to feet per minute.

a) Conversion of linear speed:
60 miles per hour = 60 * 5280 feet per hour
= 316800 feet per hour

Since there are 60 minutes in an hour:
316800 feet per hour / 60 = 5280 feet per minute

Now, to find the angular speed of the wheels in radians per minute, we need to determine how many revolutions the wheels make per minute.

b) Conversion of revolutions per minute:
The perimeter of the wheel (circumference) can be found using the diameter.
Circumference = π * diameter
= π * 2.5 feet
= 7.85 feet

Since the car is moving at a rate of 5280 feet per minute:
5280 feet per minute / 7.85 feet = 672 revolutions per minute (approximately)

Therefore:
a) The angular speed of the wheels is approximately 5280 feet per minute.
b) The wheels are rotating approximately 672 revolutions per minute.

To find the angular speed of the wheels in radians per minute, we need to determine how many radians the wheel turns in one minute. We can find this by considering that the car travels at a speed of 60 miles per hour and the diameter of the wheels is 2.5 feet.

a) Angular speed is defined as the angle traveled by an object in a unit of time. Since the car travels a distance of 60 miles in 1 hour, we can find the distance covered by the car in 1 minute by dividing 60 miles by 60 minutes, which gives us 1 mile per minute.

Since the diameter of the wheels is 2.5 feet, the circumference of the wheel is given by 2πr, where r is the radius of the wheel. We can find the radius by dividing the diameter by 2, so the radius is 2.5 feet / 2 = 1.25 feet.

Now, to find the circumference of the wheel, we multiply the radius by 2π:
Circumference = 2π * 1.25 = 2.5π feet

If the car travels one mile in one minute, it means that it has covered a distance of 5280 feet. Therefore, we can find the number of revolutions in one minute by dividing the distance (5280 feet) by the circumference of the wheel (2.5π feet).

b) Number of revolutions per minute = Distance traveled / Circumference of the wheel
Number of revolutions per minute = 5280 feet / (2.5π feet)
Number of revolutions per minute ≈ 2112 / π ≈ 672.73 revolutions per minute

So, the angular speed of the wheels is approximately 672.73 revolutions per minute.