Question

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?
A. The slope of the graph multiplied by the disk’s radius will equal the change in angular speed.
B. The area under the graph multiplied by the disk’s radius will equal the change in angular speed.
C. The slope of the graph divided by the disk’s rotational inertia will equal the change in angular speed.
D. The area under the graph divided by the disk’s rotational inertia will equal the change in angular speed.
E. The area under the graph multiplied by the disk's rotational inertia will equal the change in angular speed.

Answer 1

To calculate the increase in angular speed of a disk from a torque-time graph, one should find the area under the graph and divide it by the disk's rotational inertia.

Step-by-step explanation:

To determine how much the disk's angular speed increases during the manufacturing process using the graph of torque as a function of time, you need to focus on the area under the graph. Since torque (T) is related to angular acceleration (α) by the equation T = Iα, where I is the rotational inertia, and angular acceleration is the rate of change of angular velocity (ω), the integration of torque over time gives us the change in angular momentum, which is Iδω. To find the change in angular speed, use option D: the area under the graph divided by the disk's rotational inertia will equal the change in angular speed.