Question

The wheels on a skateboard have a diameter of 2.93 inches. If a skateboarder is traveling downhill at 23 miles per​ hour, determine the angular velocity of the wheels in radians per second.

Answer 1

The angular velocity of the wheels of the skateboard traveling downhill at 23 miles per hour is approximately 27.508 radians per second.

Step-by-step explanation:

The angular velocity of the wheels can be calculated by first converting the speed from miles per hour to inches per second. Since there are 5280 feet in a mile, we can convert 23 miles per hour to inches per second by multiplying by 5280 and dividing by 60 and 60. This gives us a speed of approximately 40.267 inches per second.

Next, we need to convert this linear velocity to angular velocity. The formula for angular velocity is given by:

Angular velocity = Linear velocity / Radius

For the given skateboard wheels with a diameter of 2.93 inches, the radius is half of the diameter, which is 1.465 inches.

Using the formula, we can calculate the angular velocity as:

Angular velocity = 40.267 inches per second / 1.465 inches = 27.508 radians per second

Answer 2

The angular velocity of the wheels is 276.314 radians per second.

Step-by-step explanation:

The wheels are rolling, which is a combination of rotation and translation, whose center of rotation is the point of contact between the wheel and the ground and the geometrical center of the skateboard experiments pure translation. Then, the angular velocity can be found by using the following kinematic expression:

`\omega = (v)/(R)` (1)

Where:

`\omega` - Angular velocity, in radians per second.

`v` - Velocity of the wheel at its center, in inches per second.

`R` - Radius of the wheel, in inches.

If we know that
`v = 404.8\,(in)/(s)` and
`R = 1.465\,in`, then the angular velocity of the wheels are:

`\omega = (404.8\,(in)/(s) )/(1.465\,in)`

`\omega = 276.314\,(rad)/(s)`

The angular velocity of the wheels is 276.314 radians per second.