Uniform cicular motion is used in physics to describe the motion of an object traveling at a constant speed in a circle. The speed of the object is called tangential velocity and it can be calculated using the formula abovce, where r is the radius of the circle and T is the time is takes for the object to make one complete circle, called a peroid. WHich of the following formulas could be used to find the length of one period if you know the tengential velocity and the radius of the circle ?

Options

A. `T= (v)/(2pir)`
B. `T=(2pir)/(v)`
C. `T= 2pirv`
D. `T=(1)/(2pirv)`

Explanation

To find the length of one period (T) in terms of tangential velocity (v) and the radius (r) of a circle, we start with the formula for tangential velocity in uniform circular motion:

1. **Start with the formula for tangential velocity**:
\[ v = \frac{2\pi r}{T} \]

2. **Rearranging the formula to solve for T**:
- Multiply both sides by T:
\[ vT = 2\pi r \]
- Now, divide both sides by v to isolate T:
\[ T = \frac{2\pi r}{v} \]

3. **Final expression for the period**:
- The formula we derived shows that the period T can be expressed as:
\[ T = \frac{2\pi r}{v} \]

4. **Identify the correct option**:
- From the options given, we see that:
- Option 1: \( T = \frac{v}{2\pi r} \) (Incorrect)
- Option 2: \( T = \frac{2\pi r}{v} \) (Correct)
- Option 3: \( T = 2\pi r \cdot v \) (Incorrect)
- Option 4: \( T = \frac{1}{2\pi r v} \) (Incorrect)
- Therefore, the correct option is **Option 2: \( T = \frac{2\pi r}{v} \)**.