A small motor delivers 0.25 hp when its shaft is turning at 1200 rev/min. Compute the torque.

To calculate the torque delivered by the motor, we can use the formula:

\[
P = T \cdot \omega
\]

Where:
- \(P\) is the power (in watts),
- \(T\) is the torque (in newton-meters),
- \(\omega\) is the angular velocity (in radians per second).

### Step 1: Convert power from horsepower to watts

1 horsepower (hp) = 746 watts, so:
\[
P = 0.25 \, \text{hp} = 0.25 \times 746 = 186.5 \, \text{W}
\]

### Step 2: Convert the angular velocity from revolutions per minute (rev/min) to radians per second

1 revolution = \(2\pi\) radians, and there are 60 seconds in a minute, so:
\[
\omega = \frac{1200 \, \text{rev/min} \times 2\pi}{60} = 125.66 \, \text{rad/s}
\]

### Step 3: Solve for torque \(T\)

Using the formula \(P = T \cdot \omega\), we rearrange to solve for torque:
\[
T = \frac{P}{\omega} = \frac{186.5 \, \text{W}}{125.66 \, \text{rad/s}} = 1.484 \, \text{N}\cdot\text{m}
\]

Thus, the torque is approximately \(1.48 \, \text{N}\cdot\text{m}\).

Would you like more details or have any questions?

Here are some related questions:
1. How do you convert angular velocity from radians per second to revolutions per minute?
2. What is the relationship between torque and power in rotational systems?
3. How would the torque change if the speed of the motor were doubled?
4. What other factors, besides power and speed, affect the torque of a motor?
5. How does horsepower relate to watts, and why do engineers often use both units?

**Tip:** Always ensure to use consistent units (watts for power and radians per second for angular velocity) when applying rotational formulas like \(P = T \cdot \omega\).

Learn how to calculate the torque of a motor delivering 0.25 hp at 1200 rev/min with a detailed solution. The problem involves converting power from horsepower to watts, angular velocity from rev/min to rad/s, and using the formula P = T * ω to solve for torque. Suitable for high school students in Grades 10-12.

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