A group of students must conduct an experiment to determine how the location of an applied force on a classroom door affects its rotational motion. The rotational inertia of the door about its hinges is known. The initial angular velocity of the door is zero.
Question: Which of the following lists what measuring devices the students need and the measurements they should take to collect the necessary data to test the relationship between a torque exerted on the door and the change in angular velocity of that object about the hinges of the door? Justify your selection.
A stopwatch to measure the time interval during which the force is applied, a force probe to measure the applied force on the door, a protractor to measure the angular displacement of the door, and a meterstick to measure the radial distance from the door’s hinges to the location where the force is applied.
To determine the relationship between the torque exerted on the door and the change in its angular velocity about the hinges, the students need to measure the force applied, the distance from the hinges at which the force is applied, and the resulting angular acceleration of the door. The angular acceleration can be determined by measuring the time it takes for the door to rotate through a certain angle.
The most appropriate list of measuring devices and measurements is:
(1) A force sensor to measure the force applied to the door
(2) A meter stick to measure the distance from the hinges to the point where the force is applied
(3) A stopwatch to measure the time it takes for the door to rotate through a certain angle
(4) A protractor to measure the angle through which the door rotates
Justification:
(1) The force sensor is necessary to measure the magnitude of the force applied to the door, which is required to calculate the torque.
(2) The meter stick is used to measure the distance from the hinges to the point where the force is applied. This distance is the lever arm, which is necessary to calculate the torque using the formula: torque = force × lever arm.
(3) The stopwatch is used to measure the time it takes for the door to rotate through a certain angle. This information is necessary to calculate the angular acceleration using the formula: angular acceleration = change in angular velocity ÷ time.
(4) The protractor is used to measure the angle through which the door rotates. This angle, along with the time measured by the stopwatch, is used to calculate the change in angular velocity.
With these measurements, the students can calculate the torque applied to the door and the resulting angular acceleration. By varying the location of the applied force (i.e., the lever arm) and keeping the force constant, they can investigate how the torque affects the angular acceleration and, consequently, the change in angular velocity of the door.