A motor has a speed of 1200 RPM and a torque of 2 N.T The power output will be:

Question

A motor has a speed of 1200 RPM and a torque of 2 N.T  The power output will be:

BlackTom AI · Accepted Answer

Power equals torque multiplied by angular velocity, so P = τ · ω. Here torque τ = 2 N·m and speed N = 1200 rpm, so we must convert rpm to angular velocity in radians per second.

Relevant concepts:
- Mechanical power (in watts) = torque (N·m) × angular speed (rad/s).
- Angular speed ω (rad/s) = 2π × (rotational speed in revolutions per second).
- Revolutions per second = rpm / 60.

Step-by-step calculation with intermediate steps:
1. Convert rpm to revolutions per second:
   N_rev/s = 1200 rpm ÷ 60 = 20 rev/s.
2. Convert revolutions per second to radians per second:
   ω = 2π × 20 = 40π rad/s.
3. Compute power:
   P = τ × ω = 2 N·m × 40π rad/s = 80π W.
4. Numerical evaluation:
   π ≈ 3.14159265 → P ≈ 80 × 3.14159265 = 251.3274123 W.

Why this answer is correct:
- The derivation uses the fundamental relation between torque and angular velocity; units are consistent (N·m × rad/s = N·m·rad/s = J/s = W).
- The exact symbolic result is 80π W, and its numerical value (~251.327 W) matches the provided value 251.32 W when reported to two decimal places (251.32 W if truncated, 251.33 W if rounded to nearest hundredth). The small difference is only due to rounding conventions, not the method.

Why other choices would be incorrect:
- A common mistake is treating rpm directly as rad/s (omitting the 2π/60 factor), which would under- or overestimate power by a factor of 2π/60.
- Another error is mixing units (e.g., using torque in different units) or forgetting to convert rpm to rev/s first; any such misstep yields an incorrect numeric result.

Conclusion:
Using P = τ·ω with ω = 2π·(1200/60) gives P = 80π ≈ 251.327 W, which corresponds to the provided answer 251.32 W.

A motor has a speed of 1200 RPM and a torque of 2 N.T The power output will be:Single choice

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