High School

A flywheel has a diameter of 1.41 m and a mass of 838 kg. What torque in newtons is needed to produce an angular acceleration of 93 rpm/s?

Answer :

Final answer:

To find the torque needed to produce an angular acceleration of 93 rpm/s for a flywheel with specific dimensions and mass, follow the steps of converting the acceleration to radian/s, calculating the moment of inertia, and applying the torque formula. In this case, the torque required would be 2021.91 N.m.

Explanation:

To determine the torque needed to produce the specified angular acceleration on the flywheel.

To find the torque needed to produce an angular acceleration of 93 rpm/s:

  1. First, convert the angular acceleration to radian/s: 93 rpm/s * 2π/60 = 9.74 rad/s²
  2. Calculate the moment of inertia of the flywheel: I = 1/2 * m * r^2 = 1/2 * 838 kg * (0.705 m)^2 = 207.56 kg.m²
  3. Use the formula for torque: τ = I * α = 207.56 kg.m² * 9.74 rad/s² = 2021.91 N.m

Therefore, 2021.91 N.m torque is needed .