Angular speed of a rotating object that results in translational motion without slipping is the ratio of the linear speed to the radius of a rotating object
The angular speed of the wheels is approximately 1,625 radians per min
The process by which the above value is arrived at is as follows:
The given parameters are;
The diameter of the wheel of the bicycle = 26 inches
The translational speed of the bicycle, v = 20 miles per hour
The required parameter:
The angular speed of the wheels in radians per minute
Method:
The units of the speed in miles per hour is converted to inches per minute, and the result is divided by the radius of the wheel, which is half the diameter
Solution:
To convert miles per hour to inches per minute we have;
1 mile = 63,360 inches
1 hour = 60 minutes
Therefore;
20 mi/hr = 20 mi/hr × 63,360 inches/mile × 1 hr/(60 min) = 21,120 in/min
∴ The translational speed, v = 20 mi/hr = 21,120 in/min
The radius of the wheel, r = D/2
∴ r = 26 inches/2 = 13 inches
Angular speed, ω = v/r
Therefore, the angular ;
[tex]\mathbf{The \ angular \ speed \ of \ the \ wheels, \ \omega} = \dfrac{21,120\dfrac{in.}{min} }{13 \ in.} \approx \mathbf{1,624.615} \ \dfrac{rad}{min}[/tex]
The angular angular speed of the bicycle wheels, given to the nearest whole number, ω ≈ 1,625 rad/min
Learn more about angular speed here:
https://brainly.com/question/16755118
