wheels on a skateboard are 3.63 inches. If the skateboarder is travelling down a hill at 23 miles per hour what is the angular velocity.
You don't say is 3.63 inches is the diameter or the radius of the wheels.
I will assume it is the diameter.
First do some speed conversions.
V = 23 mph = 33.73 ft/s = 404.8 inch/s
= R*w
w = 404.8/1.815 = 223 rad/s
To find the angular velocity of the skateboarder, we first need to convert the speed from miles per hour to inches per second because the wheel size is given in inches.
1 mile = 5,280 feet
1 foot = 12 inches
1 hour = 60 minutes
1 minute = 60 seconds
Therefore, to convert miles per hour to inches per second, we can use the following conversions:
1 mile per hour = (5,280 feet / 1 mile) * (12 inches / 1 foot) * (1 hour / 60 minutes) * (1 minute / 60 seconds)
Now, let's do the calculation:
speed in inches per second = (23 miles/hour) * (5,280 feet/mile) * (12 inches/foot) * (1 hour/60 minutes) * (1 minute/60 seconds)
speed in inches per second = 23 * 5280 * 12 / 60 / 60
speed in inches per second ≈ 121.92 inches/second
Now that we have the speed in inches per second, we can calculate the angular velocity.
Angular velocity is defined as the linear velocity divided by the wheel radius (assuming the skateboarder is moving in a straight line).
Angular velocity (in radians per second) = linear velocity (in inches per second) / wheel radius (in inches)
Since the wheel radius is given as 3.63 inches and the linear velocity is approximately 121.92 inches per second, we can calculate the angular velocity:
Angular velocity = 121.92 inches/second / 3.63 inches
Angular velocity ≈ 33.62 radians/second
So the angular velocity of the skateboarder is approximately 33.62 radians per second.