A truck with 48-in.-diameter wheels is traveling at 55 mi/h.
Find the angular speed of the wheels in rad/min, *hint convert miles to inches & hours to minutes: __rad/min
How many revolutions per minute do the wheels make?__ rpm
radius of wheel = 24 inches
one rotation = 2π(24) = 48π inches
in 1 hour it goes 55 miles
= 55x5280x12 inches
= 3484800 inches
number of rotations per hour
= 3484800/(48π) = 23109.29774 rotations per hour
= 385.155 rpm
= 385.155x(2π) radians /min
= 2420 radians/min
check my arithmetic
A truck with 2.5-foot-diameter wheels is traveling at 55 miles/hr. Find the angular speed of the wheels in degrees/min: How many revolutions per minute do the wheels make?
Oh, I see we're taking a spin with some wheel calculations! Let's strap in and have some fun!
To find the angular speed of the wheels in rad/min, we can start by converting the speed from miles per hour to inches per minute.
So, 55 mi/h is equal to 55 * 5280 * 12 inches/min (since 1 mile = 5280 feet, and 1 foot = 12 inches).
Next, we'll find the circumference of the wheel. The formula for circumference is C = π * d, where d is the diameter of the wheel.
So, the circumference of the wheel is C = π * 48 inches.
To find the angular speed, we can divide the speed in inches/min by the circumference in inches.
Angular speed = (55 * 5280 * 12) / (π * 48)
And voila! The angular speed of the wheels in rad/min is approximately __ rad/min. (I'll let you calculate the exact value, you know, for that extra spin of excitement!)
Now, finally, let's calculate the number of revolutions per minute. Since one revolution is equal to one circumference, we can divide the speed in inches/min by the circumference of the wheel in inches.
Revolutions per minute = (55 * 5280 * 12) / (π * 48)
And there you have it! The wheels make approximately __ revolutions per minute. (Time for a round of applause for those wonderful wheels!)
Remember, these calculations are all in good humor, but I'm confident you'll get the hang of it!
To find the angular speed of the wheels in rad/min, we need to first convert the speed from miles per hour to inches per minute.
1 mile = 5280 feet
1 mile = 5280 * 12 inches
1 hour = 60 minutes
So, the speed of the truck in inches per minute can be calculated as follows:
55 miles/hour * 5280 feet/mile * 12 inches/foot * 1 hour/60 minutes = X inches/minute
Let's calculate this:
55 * 5280 * 12 / 60 = X
X = 69,120 inches/minute
Now, we need to find the circumference of the wheel. The circumference is equal to the diameter multiplied by pi (π). Given that the diameter of the wheel is 48 inches, the circumference can be calculated as follows:
Circumference = 48 inches * π
Let's calculate this:
Circumference = 48 * π
Circumference ≈ 150.796 inches
The angular speed of the wheels in rad/min can be found by dividing the speed of the truck in inches per minute by the circumference of the wheel:
Angular speed = X inches/minute / Circumference
Let's calculate this:
Angular speed = 69,120 inches/minute / 150.796 inches
Angular speed ≈ 458.175 rad/min (rounded to three decimal places)
Therefore, the angular speed of the wheels is approximately 458.175 rad/min.
To find the number of revolutions per minute (rpm) that the wheels make, we can convert the angular speed to revolutions per minute. Since one revolution is equal to 2π radians, the number of revolutions can be calculated as follows:
Revolutions per minute = Angular speed in rad/min / (2π)
Let's calculate this:
Revolutions per minute = 458.175 rad/min / (2π)
Revolutions per minute ≈ 72.935 rpm (rounded to three decimal places)
Therefore, the wheels make approximately 72.935 revolutions per minute.
To find the angular speed of the wheels in rad/min, we need to convert the given values of speed and wheel diameter into consistent units.
1. Convert the speed from miles per hour to inches per minute:
- There are 5280 feet in a mile and 12 inches in a foot, so there are 5280 * 12 = 63,360 inches in a mile.
- Since there are 60 minutes in an hour, we divide the speed in miles per hour by 60 to get the speed in miles per minute.
- Finally, to convert the speed from miles per minute to inches per minute, we multiply by the number of inches in a mile (63,360).
Therefore, the speed in inches per minute is: 55 mi/h * (63,360 in/mi) / (60 min/h) = 57,744 in/min.
2. Calculate the circumference of the wheel:
- The circumference of a circle can be found using the formula C = π * d, where C is the circumference and d is the diameter.
- Since the wheel's diameter is given as 48 inches, the circumference is C = π * 48 = 150.796 square inches (approximately).
3. Determine the angular speed in rad/min:
- The angular speed is calculated by dividing the linear speed (in inches per minute) by the circumference (in inches).
- Therefore, the angular speed in rad/min is: 57,744 in/min / 150.796 in/rev ≈ 383.23 rev/min.
So, the angular speed of the wheels is approximately 383.23 rad/min.
To find the number of revolutions per minute (rpm), we need to divide the angular speed in rev/min by 2π (since one revolution equals 2π radians).
Therefore, the number of revolutions per minute is: 383.23 rev/min / (2π) ≈ 61.06 rpm.