Final answer:
The angular speed of the wheels is approximately 75.30 rad/s when the bicyclist reaches 12.0 m/s
Step-by-step explanation:
To determine the angular speed of the wheels when the bicyclist reaches 12.0 m/s, we can use the formula:
ω = ω0 + αt
Where:
- ω is the final angular speed
- ω0 is the initial angular speed, which is 0 since the bicyclist starts at rest
- α is the constant angular acceleration, which is given as 1.70 rad/s²
- t is the time taken to reach the final speed
We can calculate t using the formula:
v = v0 + at
Where:
- v is the final linear speed, which is 12.0 m/s
- v0 is the initial linear speed, which is 0 since the bicyclist starts at rest
- a is the linear acceleration, which can be calculated using the formula a = αr, where r is the radius of the wheel
Given that the diameter of the wheel is 37.5 cm, the radius can be calculated as 37.5 cm ÷ 2 = 18.75 cm = 0.1875 m.
Plugging in the values, we get:
t = (v - v0) / a = (12.0 m/s - 0 m/s) / (1.70 rad/s² * 0.1875 m) ≈ 44.29 s
Now we can calculate the final angular speed:
ω = ω0 + αt = 0 + 1.70 rad/s² * 44.29 s ≈ 75.30 rad/s