Q1. An object travels around a circle 10.0 full turns in 2.5 seconds. Calculate the angular displacement, θ in radians.

show detailed solution which includes, GRESA, given, required, equation, solution, and answer

To solve the problem, let's follow the GRESA method step-by-step: Given, Required, Equation, Solution, and Answer.

### **GRESA Method:**

1. **Given (G):**
   - The object completes 10.0 full turns.
   - Time taken is 2.5 seconds.
   
2. **Required (R):**
   - We need to find the **angular displacement** (\( \theta \)) in radians.

3. **Equation (E):**
   - The angular displacement for one full turn in radians is \( 2\pi \) (since one complete revolution equals \( 2\pi \) radians).
   - Therefore, the total angular displacement for multiple turns is:
   \[
   \theta = 2\pi \times (\text{number of turns})
   \]

4. **Solution (S):**
   - We are given 10.0 full turns, so substituting this into the formula:
   \[
   \theta = 2\pi \times 10.0
   \]
   - Simplifying the expression:
   \[
   \theta = 20\pi
   \]
   - Approximating \( \pi \) as 3.1416, we get:
   \[
   \theta = 20 \times 3.1416 = 62.832 \, \text{radians}
   \]

5. **Answer (A):**
   \[
   \theta = 62.832 \, \text{radians}
   \]

### Final Answer:
The angular displacement, \( \theta \), is **62.832 radians**.

Would you like more details or explanations on any part?  
Here are 5 related questions:

1. How would the answer change if the object completed 15 full turns?
2. What is the angular velocity of the object given the time and angular displacement?
3. How do we convert radians to degrees if required?
4. What is the significance of angular displacement in circular motion?
5. How do we apply angular displacement to real-world situations, like a spinning wheel?

**Tip:** Angular displacement is always measured in radians when working in scientific contexts involving rotational motion, as it directly relates to the geometry of a circle.

An object travels around a circle 10.0 full turns in 2.5 seconds. Calculate the angular displacement, θ in radians.

Learn how to calculate the angular displacement of an object that completes 10 full turns in 2.5 seconds. The solution involves the formula for angular displacement using radians and provides a detailed step-by-step explanation. Ideal for students in Grades 9-12 studying circular motion.

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