The wheels of a scooter have a diameter of 4.5 inches. If the person riding the scooter is traveling down hill at 15.0 mph. what is the approximate angular speed of the wheels in radians per second
Circumference = pi*D = 3.14 * 4.5 = 14.13 In. = 1.1775 Ft
V=15mi/h * 5280Ft/mi * 6.28Rad/1.1775Ft
* 1h/3600s. = 117.3 Rad/s.
<'ea14
Well, well, well, look who's scooting downhill! Let's do some math to keep up with the speed demons, shall we? Now, we know that the diameter of the wheels is 4.5 inches, which means the radius is half of that, or 2.25 inches.
To calculate the approximate angular speed of the wheels, we need to convert the speed from miles per hour to inches per second. There are 5280 feet in a mile and 12 inches in a foot, so there are 63360 inches in a mile. Dividing 15 mph by that, we get the speed in inches per second.
15 mph = 15 * 63360 inches / 3600 seconds = 264 inches per second.
Now that we have the speed in inches per second and the radius in inches, we can calculate the angular speed. The formula for angular speed is:
Angular speed = Linear speed / Radius.
Angular speed = 264 inches per second / 2.25 inches.
Let's do the math, shall we?
Angular speed ≈ 117.33 radians per second.
So there you go, my speedy friend! The approximate angular speed of your scooter's wheels is approximately 117.33 radians per second. Keep on rollin' while I keep on clownin'!
To find the angular speed of the wheels in radians per second, we first need to calculate the linear speed of the scooter in inches per second.
The linear speed is the distance traveled per unit of time, which can be calculated using the formula:
Linear Speed = (Angular Speed) x (Radius)
Given that the diameter of the wheels is 4.5 inches, the radius would be half of the diameter, which is 2.25 inches.
Linear Speed = 15.0 mph * (5280 ft/mile) * (12 in/ft) / (3600 s/h)
Linear Speed = 22 ft/s
Now, we can find the angular speed in radians per second. The formula to convert from linear speed to angular speed is:
Angular Speed (in radians per second) = Linear Speed (in inches per second) / Radius (in inches)
Angular Speed = 22 ft/s * (12 in/ft) / 2.25 in
Angular Speed ≈ 117.33 radians per second
Therefore, the approximate angular speed of the wheels is approximately 117.33 radians per second.
To find the approximate angular speed of the wheels in radians per second, we need to convert the linear speed of the scooter to angular speed.
First, let's convert the linear speed from miles per hour to inches per second:
15.0 mph * (5280 feet / 1 mile) * (12 inches / 1 foot) * (1 hour / 3600 seconds) = 22 inches/second (approximately).
Next, let's find the circumference of the wheel using its diameter:
Circumference = π * diameter = π * 4.5 inches.
Now that we know the linear speed and the circumference, we can find the number of revolutions per second. Since the circumference is covered in one revolution:
Revolutions per second = 22 inches/second / (π * 4.5 inches).
Finally, to convert the revolutions per second to radians per second, we can use the fact that 1 revolution is equivalent to 2π radians:
Angular speed in radians per second = (22 inches/second / (π * 4.5 inches)) * (2π radians / 1 revolution).
After canceling units and simplifying, the approximate angular speed of the wheels in radians per second can be calculated.