Calculate Instantaneous Rotational Power

Calculating Instantaneous Rotational Power of a Torque

In this scenario, a torque of 100 N-m is acting on a rotating object. At a specific instant, the object is rotating with an angular velocity of 120 rpm. We need to determine the instantaneous rotational power of the torque at that moment.

Options:

a. 400 watt

b. 12000/π watt

c. 120/π watt

d. 40 watt

Final answer:

The instantaneous rotational power of a torque can be calculated using the formula P = Tw, where P is the power, T is the torque, and w is the angular velocity. Plugging in the given values, we can calculate that the instantaneous rotational power is 400π watt. Therefore, the correct answer is: (a).

Explanation:

The instantaneous rotational power of a torque at a given instant can be calculated using the formula P = Tw, where P is the power, T is the torque, and w is the angular velocity.

In this case, the torque is given as 100 N-m and the angular velocity is 120 rpm. To convert the angular velocity from rpm to rad/s, we can use the formula w = (2π/60) * angular velocity. Plugging in the values, we get w = (2π/60) * 120 = 4π rad/s.

Now, we can calculate the power using the formula P = Tw = (100 N-m) * (4π rad/s) = 400π watt. So, the correct answer is option a. 400 watt.