We can solve this problem using the equations of angular motion. The flywheel starts from rest, so the initial angular velocity $\omega_0 = 0 \, \text{rad/s}$. The angular acceleration $\alpha = 0.5 \, \text{rad/s}^2$ and the time $t = 10 \, \text{seconds}$.

1. Angular velocity ($\omega$) after 10 seconds:

The formula for angular velocity after time $t$ when starting from rest is: $\omega = \omega_0 + \alpha t$ Substitute the values: $\omega = 0 + (0.5 \, \text{rad/s}^2)(10 \, \text{s}) = 5 \, \text{rad/s}$

2. Angular displacement ($\theta$) after 10 seconds:

The formula for angular displacement when starting from rest is: $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$ Substitute the values: $\theta = 0 + \frac{1}{2} (0.5 \, \text{rad/s}^2)(10^2 \, \text{s}^2) = \frac{1}{2} \times 0.5 \times 100 = 25 \, \text{radians}$

Summary:

• Angular velocity after 10 seconds: $5 \, \text{rad/s}$
• Angular displacement after 10 seconds: $25 \, \text{radians}$

Would you like further details on any of these calculations?

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Here are 5 related questions to expand your understanding:

1. What would happen if the angular acceleration were doubled?
2. How would you calculate the total number of revolutions instead of angular displacement?
3. What is the difference between linear and angular acceleration?
4. How does angular velocity change over time if the acceleration is constant?
5. What factors affect the angular acceleration of a flywheel in real-world scenarios?

Tip: Always check the units of angular acceleration and time before plugging them into the equations to avoid errors.