Question 13 of 16intermediate🔧 ApplyNumerical2 marks

To maintain a rotor at a uniform angular speed of 200 rad s⁻¹, an engine needs to transmit a torque of 180 N m. What is the power required by the engine? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is 100% efficient.

Correct Answer

The power required by the engine is 36 kW (or 36000 W).

Exercise: EXERCISES | Q: 6.14 | (Page 35)
For More Understanding

Explanation

To maintain a rotor at a uniform angular speed, the engine must apply a torque to counteract friction. The power required for rotational motion is determined by the product of the applied torque and the angular velocity. The context provides the relationship involving torque and angular velocity in the form of the equation τω=Iωα\tau \omega = I \omega \alpha, where the term τω\tau \omega represents the power delivered to the system. By substituting the given values of torque and angular speed into this relationship, we can calculate the required power.

Solution Steps

  1. Step 1: Identify the given values. Angular speed (ω\omega) = 200200 rad s⁻¹ Torque (τ\tau) = 180180 N m

  2. Step 2: Identify the formula for Power. From the relation provided in the context (τω=Iωα\tau \omega = I \omega \alpha), the power (PP) is given by the product of torque and angular speed:

    P=τωP = \tau \omega

  3. Step 3: Calculate the Power.

    P=180 N m×200 rad s−1P = 180 \text{ N m} \times 200 \text{ rad s}^{-1} P=36000 WP = 36000 \text{ W} P=36 kWP = 36 \text{ kW}
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