Question

A rotating flywheel has a moment of inertia of 15.0 kg ��� m�� for an axis along the axle about which the wheel is rotating. Initially, the flywheel has 30.0 J of kinetic energy. It is slowing down with an angular acceleration of magnitude 0.700 rev/s��. What is the torque acting on the flywheel?

1) 0.700 N ��� m
2) 2.100 N ��� m
3) 4.200 N ��� m
4) 6.300 N ��� m

Answer 1

The torque acting on the flywheel is calculated using the formula τ = I × α, considering the moment of inertia and angular acceleration. However, the calculated torque of 66.0 N·m does not match any of the given answer choices, suggesting a discrepancy in the question or answers.

Step-by-step explanation:

The student asks about the torque acting on a flywheel, given its moment of inertia, initial kinetic energy, and the magnitude of its angular acceleration.

To find the torque (τ), we can use the relationship between torque, moment of inertia (I), and angular acceleration (α):

τ = I × α

First, we need to convert the angular acceleration from revolutions per second squared to radians per second squared since SI units are required.

1 rev = 2π radians

0.700 rev/s² = 0.700 × 2π rad/s²

0.700 rev/s² = 4.398 rad/s²

Now we can calculate the torque:

τ = 15.0 kg·m² × 4.398 rad/s²

τ = 66.0 N·m

However, the options provided in the question do not include this value, which indicates a possible error in the question or the provided answer choices.