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.