1. A wheel is spinning so that it goes around 6 times every second. A brake is then applied to the wheel, causing it to slow to a frequency of 3 times per second in 5 seconds. How many times does the wheel spin around while the brake is applied? Fill in the table with what is given and what is needed. All values in the table should be in terms of radians. ΔΘ @; Of α At X

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**Problem Statement:**

1. A wheel is spinning so that it goes around 6 times every second. A brake is then applied to the wheel, causing it to slow to a frequency of 3 times per second in 5 seconds. How many times does the wheel spin around while the brake is applied?

**Instructions:**

Fill in the table with what is given and what is needed. All values in the table should be in terms of radians.

**Table:**

| Symbol | Description          | Value in Radians |
|--------|----------------------|------------------|
| \(\Delta \theta\) | Angular displacement   |                  |
| \(\omega_i\)      | Initial angular velocity |                  |
| \(\omega_f\)       | Final angular velocity   |                  |
| \(\alpha\)         | Angular acceleration    |                  |
| \(\Delta t\)       | Time interval          |                  |

**Explanation:**

- \(\Delta \theta\): This represents the total angular displacement of the wheel while the brake is applied.
- \(\omega_i\): This is the initial angular velocity of the wheel, which relates to how fast it was spinning before the brake was applied.
- \(\omega_f\): This is the final angular velocity after the brake has been applied, when the wheel slows down.
- \(\alpha\): This represents the angular acceleration, or how quickly the wheel is slowing down.
- \(\Delta t\): This is the time interval during which the brake is applied.

Each of these parameters is essential for analyzing the motion of the wheel and understanding how the application of the brake affects its rotational speed.
Transcribed Image Text:**Problem Statement:** 1. A wheel is spinning so that it goes around 6 times every second. A brake is then applied to the wheel, causing it to slow to a frequency of 3 times per second in 5 seconds. How many times does the wheel spin around while the brake is applied? **Instructions:** Fill in the table with what is given and what is needed. All values in the table should be in terms of radians. **Table:** | Symbol | Description | Value in Radians | |--------|----------------------|------------------| | \(\Delta \theta\) | Angular displacement | | | \(\omega_i\) | Initial angular velocity | | | \(\omega_f\) | Final angular velocity | | | \(\alpha\) | Angular acceleration | | | \(\Delta t\) | Time interval | | **Explanation:** - \(\Delta \theta\): This represents the total angular displacement of the wheel while the brake is applied. - \(\omega_i\): This is the initial angular velocity of the wheel, which relates to how fast it was spinning before the brake was applied. - \(\omega_f\): This is the final angular velocity after the brake has been applied, when the wheel slows down. - \(\alpha\): This represents the angular acceleration, or how quickly the wheel is slowing down. - \(\Delta t\): This is the time interval during which the brake is applied. Each of these parameters is essential for analyzing the motion of the wheel and understanding how the application of the brake affects its rotational speed.
Expert Solution
Step 1

frequency of the spinning wheel, f1=6 Hz

frequency of spinning of the wheel when breaks were applied or after retardation, f2=3 Hz

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