Extended objects can have translational and rotational motion. To describe the motion of an unconstrained object, such as a football in flight, it is most convenient to treat the motion as a combination of translational motion of the center of mass and rotational motion about the center of mass. The motion of an object constrained to rotate about a fixed axis, such as a door rotating about a vertical axis defined by its hinges, is often more conveniently described as a pure rotation about this axis. If this axis is not a symmetry axis, the object then exerts a force on the axis, and an external force is required to keep the net force on the axis zero and the axis fixed.
In this session, we will become familiar with describing rotational motion. We will investigate the relationships between angular acceleration, moment of inertia, angular momentum and torque. Finally, we will construct and examine a simple model of a forearm.
Equipment needed:
Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions. This log will form the basis of your lab report. Address the points highlighted in blue. Answer all questions.
Experiment 1
Have one person in your group stand up and make a fist. This person should then gently swing their arm in a vertical circle, pivoting at the shoulder and keeping the rest of the arm straight. Observe the motion of the arm. Pay attention to the motion of the elbow and of the hand.
Make the following measurements and record the data in your log:
Use your data to answer the following questions.
What was the average centripetal acceleration (m/s2) of the hand?
Optional Experiment
Open the Phyphox app on your phone. Click on the Gyroscope (rotation rate) sensor. This sensor measures your angular velocity ω (both its vector components and its magnitude). Click Absolute, to measure the magnitude.
Sit on a swivel chair and push against the floor for an angular impulse. Once you are rotating start taking data. After two revolutions stop taking data. Use "Pick data" on the last data point of the graph to find the time interval Δt during which you took data. The number below the graph tells you the magnitude of the average angular velocity as measured by the sensor.
Exploration
Use an on-line simulation from the University of Colorado PhET group to
investigate the relationships between angular acceleration, moment of inertia,
angular momentum and torque.
Link to the simulation:
http://phet.colorado.edu/en/simulations/torque
This is a simulation written in Java. Here are instructions on running
Java PhET simulation on a
Windows or
macOS computer.
If you cannot rum Java on your computer, run the simulation via
Cheerpj (the browser compatible version). It takes a long time to load, and it runs slower, but it works.
Click the Intro tab explore the interface.
Click the Torque tab.
Click the Moment of Inertia tab.
Click the Angular Momentum tab.
Experiment 2
Take a meter stick with a clip to which you can attach a weight. Grab the stick on one end, and
hold it horizontal, with the weight close to your hand. Then have someone slide
the weight out to other end. Does it become harder to hold the stick
horizontal? Why? You are holding up the same weight.
In this experiment, we will use the meter stick as an artificial forearm.
The arm (excluding the shoulder and wrist) is composed to two major segments. The upper arm is attached to the shoulder. The forearm is attached to the upper arm at the elbow. Let us only concentrate on situations where the upper arm is in the vertical position. Then the forearm can move in two directions, upwards or downwards.
The upper-arm and the forearm can be thought of as two rigid levers, joined at the elbow, which acts as a pivot point. Muscles attached to these levers provide the force required to articulate their motion. Since muscles can only provide force by contraction, they must always work in pairs. As the contracting muscle, (red), tightens, it applies a force to the arm. At the same time, the opposing muscle, (black), relaxes, thus allowing the arm to move. We have a pair of simple levers.
When we lift a load with our biceps muscle, this muscle does positive work.
The triceps muscle does positive work when we push down on something.
There is also a third force on the forearm, the force the upper arm's bone exerts on the forearm at the elbow joint. This force does no work, because the elbow joint is not moving.
Procedure:
Attach 3 clips to the meter stick, one at each end, and one in the middle as shown in the figure below. Hang the stick from the force sensor. Adjust the position of the center clip so the stick is horizontal. Use the force sensor and Capstone to measure the weight of the stick and the clips. (Always press the tare button on the force sensor before you attach something to the hook to make a measurement.)
Move the center clip to a position 20 - 25 cm away from the left edge of the stick. Now the stick is no longer horizontal. You have to push down on the left end of the stick to bring the stick to a horizontal position. When you push down on the stick, what happens to the reading of the force sensor?
To find out how hard you have to push down to bring the stick to a horizontal position. Attach a mass hanger to the clip on the left end. Load masses onto the mass hanger until the stick is horizontal. The combined weight of the masses and hanger equals the force with which you have to push down.
Fill in the table below. Record only magnitudes. (Before taking a force reading, remove the stick, press the tare button, and reattach the stick.)
| weight of meter stick and clips | |
|---|---|
| weight suspended from left clip | |
| (optional) weight suspended from right clip | |
| force sensor reading when the stick is again horizontal | |
| distance d from left clip to force sensor hook (pivot point) | |
| distance from force sensor hook to CM of meter stick | |
| distance from force sensor hook to right clip |
Modeling the meter stick as a forearm and the force sensor as
the biceps, compare the force that the biceps has to exert to keep the forearm
horizontal to the force it has to exert to just support the weight of the
forearm. Comment on the relative magnitude of these forces.
List all the forces (magnitude and direction) acting on the
forearm (meter stick) and calculate all the torques (magnitude and direction)
exerted by those forces about the pivot point, when the stick is horizontal and
in equilibrium. Do all the forces and torques cancel out?
Discuss this simple model and your answers
with your partners and write down questions if you have any.
Convert your log into a lab report.
Name:
E-mail address:
Laboratory 6 Report
Save your Word document (your name_lab6.docx), go to Canvas, Assignments, Lab 6, and submit your document.