A car is moving at a rate of 55 mph and the diameter of its wheels is 2 feet.
A) Find the number of revolutions per minute the wheels are rotating.
B) Find the angular speed of the wheels in radians per minutes.
To find the number of revolutions per minute the wheels are rotating, you need to convert the car's speed from miles per hour to feet per minute. Then, divide the speed by the circumference of the wheels to get the number of revolutions per minute.
To convert the speed from mph to feet per minute, use the conversion factor 1 mile = 5,280 feet and 1 hour = 60 minutes:
Speed in feet per minute = (55 miles/hour) * (5280 feet/mile) / (1 hour/60 minutes) = 55 * 5280 / 60 = 4840 feet/minute.
To calculate the circumference of the wheels, use the formula for the circumference of a circle:
Circumference = π * diameter
Given the diameter of 2 feet, the circumference is:
Circumference = π * 2 = 6.28 feet.
Finally, divide the speed in feet per minute by the circumference to find the number of revolutions per minute:
Number of revolutions per minute = Speed in feet per minute / Circumference
= 4840 feet/minute / 6.28 feet/revolution
≈ 771.34 revolutions/minute.
Thus, the wheels are rotating approximately 771.34 revolutions per minute.
To find the angular speed of the wheels in radians per minute, you need to convert the number of revolutions per minute to radians per minute.
Since one revolution is equivalent to 2π radians, multiply the number of revolutions per minute by 2π:
Angular speed in radians per minute = Number of revolutions per minute * 2π
≈ 771.34 revolutions/minute * 2π
≈ 4850.53 radians/minute.
Therefore, the angular speed of the wheels is approximately 4850.53 radians per minute.
Sure! Let's find the answers step by step:
A) To find the number of revolutions per minute the wheels are rotating, we need to determine how many times the wheels complete a full revolution in one minute.
First, let's convert the car's speed from miles per hour to feet per minute:
55 mph = 55 miles / 1 hour
= 55 miles / 60 minutes (since there are 60 minutes in an hour)
= 55 * 5280 feet / 60 minutes (since there are 5280 feet in a mile)
= 48400 feet / 60 minutes
= 806.67 feet / minute (rounded to two decimal places)
Next, we need to find the circumference of the wheel (distance traveled in one revolution). The circumference of a circle is given by the formula: C = π * d, where C is the circumference and d is the diameter.
Since the diameter of the wheels is 2 feet, the radius is half of that, which is 1 foot.
C = π * d
= π * 2 feet
= 2π feet
Now we can find the number of revolutions per minute by dividing the speed in feet per minute by the circumference:
Number of revolutions per minute = Speed in feet per minute / Circumference
= 806.67 feet / minute / 2π feet
= 806.67 / (2 * 3.14159)
= 806.67 / 6.28318
≈ 128.49 revolutions per minute (rounded to two decimal places)
Therefore, the wheels are rotating at approximately 128.49 revolutions per minute.
B) To find the angular speed of the wheels in radians per minute, we need to convert the number of revolutions per minute to radians per minute.
Since one revolution is equal to 2π radians, the angular speed is equal to the number of revolutions per minute multiplied by 2π:
Angular speed in radians per minute = Number of revolutions per minute * 2π
= 128.49 revolutions per minute * 2π
≈ 807.82 radians per minute (rounded to two decimal places)
Therefore, the angular speed of the wheels is approximately 807.82 radians per minute.
so the radius is 1 ft
and the circumference is 2π
55 mph = 55(5280)/60 ft/min
= 4840 ft/min
so rotations per min = 4840/2π
= 770.31
since 1 rotation is 2π radians
angular speed = 4840/(2π) * 2π = 4840 radians/min