So now on step one thither it's units is it not degree and I have not understood

You're right to ask for clarification on units! In Step 1, the unit is radians, not degrees. Let me explain:

• Revolutions: A revolution is one complete turn around a circle ($360^\circ$).
• Degrees: A degree is a unit of angular measurement, where a full circle is $360^\circ$.
• Radians: A radian is another unit of angular measurement. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

For calculations involving angular velocity ($\omega$) and other rotational dynamics in physics, the standard unit for angular displacement ($\Delta \theta$) is the radian. This is because radians simplify many formulas in calculus and physics (e.g., the arc length $s = r\theta$ is only true when $\theta$ is in radians).

The conversion is:

$$1 \text{ revolution} = 360^\circ = 2\pi \text{ radians}$$

So, in Step 1, we converted the given 1800 revolutions directly into radians using the conversion factor $2\pi \text{ rad/rev}$:

$$\Delta \theta = 1800 \text{ rev} \times \frac{2\pi \text{ rad}}{1 \text{ rev}} = 3600\pi \text{ rad}$$

This gives us the total angular displacement in radians, which is necessary for calculating angular velocity in rad/s.