Exploration 1: Torque
Drag the tip of the force arrow (position is given in meters and force is given in newtons). The red arrow is the radius, on which the force acts, and the dark green arrow is the force. The light green arrow also represents the force and is there to help illustrate the angle between \(\color{red}{r}\) and \(\color{green}{F}\). Restart.
- When is the cross product zero?
- What is the angle between \(\color{red}{r}\) and \(\color{green}{F}\) that goes in \(r F \sin(\theta )\)?
- Is there anything missing in this representation of the torque?
- Does the assignment of \(\color{red}{r}\) and \(\color{green}{F}\) matter? In other words, if \(\color{red}{r}\) was \(\color{green}{F}\) and \(\color{green}{F}\) was \(\color{red}{r}\), would the torque be the same?
In this Exploration you are looking down at a black ball on a table top. Drag the crosshair cursor (position is given in meters and time is given in seconds) to within \(5\text{ m}\) of the \(0.2\text{-kg}\) black ball. The cursor will then exert a constant force on the black ball. You may choose either an attractive or a repulsive force. In addition, the black ball is constrained to move in a circle by a very long wire. The blue arrow represents the net force acting on the mass, while the bar graph displays its kinetic energy in joules. Restart.
For attraction and repulsion, drag the cursor around to see the net force.
- At the beginning of the animation (after you press "play" but before you move the cursor), in what direction does the net force point?
- With this force, does the black ball move? Why or why not?
- Where must you apply the force in order to make the ball acquire a tangential velocity?
- Describe the direction of the force that makes the ball acquire the maximum tangential velocity for the force applied.
- How does the magnitude of the torque relate to the force applied?
- How does the direction of the torque relate to the force applied?
Exploration 3: Rolling Down an Incline
A solid ball of radius \(1.0\text{ m}\) rolls down an incline, as shown (position is given in meters and time is given in seconds). The incline makes an angle \(\theta\) with the horizontal. Adjust the mass (\(100\text{ g} < m < 500\text{ g}\)) and/or the angle (\(10^{\circ} <\theta < 40^{\circ}\)) and watch the graph of gravitational potential energy and rotational and translational kinetic energy vs. time or distance. Restart.
Change the angle and the mass of the ball to determine the answers to the following questions.
- What percent of the initial gravitational potential energy is converted into translational kinetic energy at the bottom of the hill?
- What percent of the initial gravitational potential energy is converted into rotational kinetic energy at the bottom of the hill?
- What is the ratio of \(KE_{\text{rot}}/KE_{\text{trans}}\)? What does this number correspond to?
- How does the ratio of \(KE_{\text{rot}}/KE_{\text{trans}}\) depend on the mass of the ball? On the angle of the incline?
- How would the animation change if the ball were replaced by a disk of the same radius?
Exploration authored by Wolfgang Christian and Mario Belloni.
Script authored by Steve Mellema, Chuck Niederriter, and Mario Belloni.
Exploration 4: Moment of Inertia and Angular Momentum
A \(1\text{-kg}\) red mass is incident on an identical black mass that is attached to a massless rigid string so that it can rotate around the origin as shown (position is shown in meters and time is shown in seconds). At \(t = 2.6\text{ s}\) the red mass undergoes a completely elastic collision with the black mass. Restart.
Watch the animation. You may vary the radius of the pendulum between \(2\) and \(10\text{ m}\). Answer the first three questions before clicking the "see other variables" check box.
- As you reduce the length of the pendulum, does the angular speed of the pendulum increase or decrease?
- From what you know about conservation laws, state whether you think linear momentum, angular momentum, and kinetic energy are conserved during the animation. Why?
- Set \(R = 5\text{ m}\). Calculate the linear momentum, angular momentum (about the origin), and kinetic energy of the system at \(t = 1,\: 2,\: 4\), and \(5\text{ s}\).
You may now click the check box.
- If your answers differ from what you thought, explain why they differ.
Exploration 5: Conservation of Angular Momentum
A man is standing beside a \(150\text{-kg}\) merry-go-round and suddenly drops a red object onto the merry-go-round (position is given in meters and time is given in seconds). You may change the mass of the object dropped on the merry-go-round and assume that the merry-go-round is a solid, uniform disk. Restart.
- What happens to the final angular velocity of the merry-go-round when a heavier object is dropped onto it?
- Is there a mass that you can add to make the final angular velocity exactly half of the initial angular velocity? If so, what is it?
- How do your answers to (a) and (b) relate to the conservation of angular momentum?
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.
