10.1 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 as follows:

1. The radius of the rim is 0.66 m. The thickness of the tyre is 0.024 m (converted from 24 mm).
2. Therefore, the total radius including the tyre is: $$ext{Total Radius} = 0.66 + 0.024 = 0.684 ext{ m}$$
3. The diameter is twice the radius: $$ext{Diameter} = 2 imes 0.684 = 1.368 ext{ m}$$

Thus, the diameter of the wheel is approximately 1.37 m.

To find the rotational frequency, we can first convert the circumferential velocity to metres per second:

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

Next, the circumference of the wheel can be calculated as:

$$C = 2 imes ext{Total Radius} imes ext{π} = 2 imes 0.684 imes ext{π} \\\ ext{Thus, } C ext{ is approximately } 4.296 ext{ m.}$$

The rotational frequency (in revolutions per second) is:

f = rac{v}{C} = rac{16.67}{4.296} \\ ext{This results in approximately } 3.87 ext{ revolutions per second.}