# What is the power needed to accelerate a flywheel?

Please see the attached file for full problem description.

I need to calculate torque for this question:

A gearbox and ﬂywheel are as shown in FIGURE 4 (attached). The output shaft rotates in the opposite direction to the input shaft at 5 times its speed. The gearbox has an eﬁiciency of 92%.

If the ﬂywheel is solid, has a mass of 50 kg, a diameter of 1.5 m and is to accelerate from rest to 300 revs min^-1 in 1 minute:

(a) Calculate the torque required at input T_1.

(b) Calculate the magnitude and direction of the torque required to hold the gearbox stationary (holding torque T_h). Show the direction of the holding torque applied to the shaft with the aid of a sketch.

(c) Plot a graph of the input power against time when taking the ﬂywheel from rest to 300 revs min^-1.

https://brainmass.com/engineering/mechanical-engineering/power-accelerate-flywheel-angular-momentum-torque-594114

#### Solution Preview

Please see the attached file for full problem description.

Solution:

(a) From the power balance, it follows that:

(Attached)

where Plost = lost power, which can be determined from the gearbox efficiency:

(Attached)

The required input torque related to the output torque will be:

(Attached)

One assumes that acceleration of flywheel is uniform, that means, in our case:

(Attached)

where t = acceleration time and (n2)max = maximum rotating speed after the given acceleration time. Based on the aforementioned assumption, the required torque to accelerate the flywheel of a given ...

#### Solution Summary

In this problem, the input torque and the needed input power is computed, given that a flywheel is accelerated from rest to a speed of n = 300 rpm during t = 1 min. The holding torque is computed as well.