A bicycle with a 26-inch diameter wheel is traveling at 20 miles per hour. Find the angular speed of the wheels, in radians per minute, rounding to the nearest whole number.

Sagot :

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

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