Answer :
Final answer:
The correct answer is option a. To calculate the linear velocity of a bicycle wheel from angular velocity, the wheel's radius is determined from its diameter, and the relationship between linear and angular velocity is applied. After conversion to the proper units, the linear velocity in miles per hour is found to be 29.1 mph.
Explanation:
To find the linear velocity of a bicycle wheel given the angular velocity and the diameter of the wheel, we first need to understand the relationship between linear velocity (\(v\)) and angular velocity (\(\omega\)). This relationship is given by the equation \(v = \omega \times r\), where \(r\) is the radius of the wheel.
First, we convert the diameter of the wheel to the radius by dividing by 2: \(28\ inches \div 2 = 14\ inches\). To convert the radius to feet, we use the conversion 1 foot = 12 inches: \(14\ inches \times \frac{1 foot}{12 inches} = 1.167 feet\).
Now we can calculate the linear velocity in feet per second: \(v = 8\ rad/s \times 1.167 feet\).
The answer will be in feet per second. To convert this to miles per hour, we use the conversion factors 1 mile = 5280 feet and 1 hour = 3600 seconds. After performing the calculations, we find that the correct answer is (a) 29.1 mph.
