**Given Data:**

- Power of the motor, P = 3 kW
- Voltage supply, V = 180 V
- Armature resistance, Ra = 0.9 Ω
- Shunt field resistance, Rsh = 110 Ω
- No-load current, I0 = 7 A
- No-load speed, N0 = 1030 rpm

**Calculations:**

1. **Armature current, Ia:**
- At no load, the motor draws a current of 7 A. This current includes the armature current (Ia) and the shunt field current (If).
- Since the shunt field current is usually small compared to the armature current, we can assume that the total current drawn is approximately equal to the armature current.
- Therefore, Ia = 7 A.

2. **No-load power, P0:**
- The no-load power can be calculated using the formula P0 = VI0, where V is the supply voltage and I0 is the no-load current.
- Substituting the given values, P0 = 180 V x 7 A = 1260 W.

3. **Mechanical power output, Pmech:**
- The mechanical power output can be calculated using the formula Pmech = P - P0, where P is the total power of the motor.
- Substituting the given values, Pmech = 3 kW - 1.26 kW = 1.74 kW.

4. **Rotational losses, Prot:**
- The rotational losses can be calculated using the formula Prot = P - Pmech, where P is the total power of the motor.
- Substituting the given values, Prot = 3 kW - 1.74 kW = 1.26 kW.

5. **Rotational losses in watts, Wrot:**
- The rotational losses can be converted from kilowatts to watts by multiplying by 1000.
- Therefore, Wrot = 1.26 kW x 1000 = 1260 W.

**Answer:**

The rotational loss of the machine is 1260 W.

**Explanation:**

The rotational losses in a motor are the losses that occur due to friction and windage. These losses are typically converted into heat and are responsible for reducing the overall efficiency of the motor.

In this question, we are given the power and voltage rating of the motor, as well as the armature and shunt field resistances. By using the given data, we can calculate the various parameters of the motor and determine the rotational losses.

We start by calculating the armature current at no load, which is equal to the current drawn by the motor. Next, we calculate the no-load power, which is the product of the supply voltage and the no-load current.

Using the total power and the no-load power, we can calculate the mechanical power output. The difference between the total power and the mechanical power output gives us the rotational losses.

Finally, we convert the rotational losses from kilowatts to watts to get the final answer. In this case, the rotational losses of the machine are found to be 1260 W.