A machine is applying a torque to rotationally accelerate a metal disk during a manufacturing process. An engineer is using a gr
aph of torque as a function of time to determine how much the disk’s angular speed increases during the process. The graph of torque as a function of time starts at an initial torque value and is a straight line with positive slope. What aspect of the graph and possibly other quantities must be used to calculate how much the disk’s angular speed increases during the process?
Question 9 A machine is applying a torque to rotationally accelerate a metal disk during a manufacturing process. An engineer is using a graph of torque as a function of time to determine how much the disk's angular speed increases during the process The graph of torque as a function of time starts at an initial torque value and is a straight line with positive slope. What aspect of the graph and possibly other quantities must be used to calculate how much the disk's angular speed increases during the process? The slope of the graph multiplied by the disk's radius will equal the change in angular speed The area under the graph multiplied by the disk's radius will equal the change in angular speed. The slope of the graph divided by the disk's rotational inertia will equal the change in angular speed. The area under the graph divided by the disk's rotational inertia will equal the change in angular speed. The area under the graph multiplied by the disk's rotational inertia will equal the change in angular speed E
(D) The area under the graph divided by the disk's rotational inertia will equal the change in angular speed.
Explanation:
Angular momentum is equal to the product of rotational inertia and angular speed. Therefore, angular speed would be angular momentum divided by rotational inertia.
Torque is the slope of angular momentum, so the area under the torque curve would be equal to the angular momentum.
In conclusion, the angular speed would be the area under the torque curve divided by the rotational inertia.
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