To determine the angle of rotation between the two hands of a clock, we use the formula:

$\theta = \frac{s}{r}$

Where:

• $\theta$ is the angle in radians,
• $s$ is the arc length, and
• $r$ is the radius of the circle.

Step 1: Substitute the given values

• $s = 0.54 \, \text{m}$,
• $r = 0.52 \, \text{m}$.

$\theta = \frac{0.54}{0.52}$

$\theta \approx 1.0385 \, \text{radians}.$

Step 2: Convert radians to degrees

To convert radians to degrees, use the formula:

$\text{Degrees} = \theta \times \frac{180}{\pi}.$

$\text{Degrees} = 1.0385 \times \frac{180}{\pi} \approx 59.5^\circ.$

Final Answer:

The angle of rotation between the two hands of the clock is approximately 59.5 degrees.

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Would you like a more detailed explanation or a step-by-step diagram?

Related Questions:

1. How do you calculate the length of an arc given the radius and angle in degrees?
2. What is the formula to convert degrees back into radians?
3. Can you explain why the relationship $\theta = \frac{s}{r}$ holds for circular motion?
4. How does the calculation change if the radius doubles but the arc length remains the same?
5. How can this formula be used in real-world scenarios, like engineering or design?

Tip: Always ensure that the radius and arc length are in the same units when applying the formula!