The picture and diagram below show the rear wheel of a training bicycle - NSC Technical Mathematics - Question 10 - 2024 - Paper 2

The diameter of the wheel can be calculated by adding twice the thickness of the tyre to the rim diameter. The rim's diameter is:

$ext{Diameter} = 2 imes 26 ext{ inches} imes 0.0254 ext{ meters/inch} + 2 imes 0.024 ext{ meters} = 0.6844 ext{ meters}$

Thus, the total diameter is approximately 1.37 meters.

To find the rotational frequency in revolutions per second, we start with the formula:

v = r imes rac{2 imes ext{π}}{T}

Where:

• $v$ is the circumferential velocity in meters per second,
• $r$ is the radius in meters,
• $T$ is the period in seconds.

Converting 60 km/h to m/s:

v = rac{60 ext{ km/h} imes 1000 ext{ m/km}}{3600 ext{ s/h}} = 16.67 ext{ m/s}

Using the radius:

$r = 0.66 ext{ m}$

The rotational frequency ($f$) in revolutions per second is calculated as:

f = rac{v}{2 imes ext{π} imes r} = rac{16.67}{2 imes ext{π} imes 0.66} \\ \\ ext{Approximately} \\ ext{f} ext{is about } 3.87 ext{ revolutions per second.}