Question

a couple 100Nm acts on the shaft of a motor and rotates it at a speed 7 rev/s.calculate the power of developed​

Answer 1

Given:

Couple is 100 Nm and Angular velocity is 7 rev/s

To find:

Power developed ?

Concept:

In case of translational motion , power developed is the product of Force and Velocity ;

Similarly in rotational motion , the power developed can be thought as the product of torque and angular velocity

Calculation:

Angular velocity is 7 rev/s = 7 × 2π = 44 rad/s

$p = torque \times ang. \: velocity$

$= > p = \tau \: \times \: \omega$

$= > p = 100 \times 44$

$= > p = 4400 \: watt$

So final answer is

Power developed is 4400 watt or 4.4 KWatt

Answer 2

Answer

Torque , τ = 100 Nm

Angular velocity , ω = 7 rev/s

We know that 1 revolution = 2π radians

⇒ ω = 7 rev/s = 7 (2π) rad/s

⇒ ω = 44 rad/s

Now power is defined as the product of torque and angular velocity .

⇒ Power , p = τ ω

⇒ p = 100 * 44

⇒ p = 4,400 watt

⇒ $\bold{\bf{\red{p = 4.4\;kilowatt }}}$

So the power developed is 4.4 kilowatt.