Optional Practical: Rotational dynamics (Algodoo)
In this exercise Algodoo will be used to simulate the rotation of a rigid body. The idea is not to test if the simulation gives the expected result (it will) but to reinforce the theory learnt in class.
Building the rigid body
To make the analysis simple a the body used will be a particle on the end of a light rod.
- Open a new scene in Algodoo choose blueprint as this will enable you to position the objects more accurately.
- Show the grid and switch off gravity and air resistance.
- Untick "snap to grid". If you don't do this you will only be able to draw objects that fit the grid lines.
- Use the box tool to draw a rectangle 5m long and 0.2 m wide, double click and tick "ruler" from the "appearance" options.
- In the materials options set the mass of the rectangle to 0.001 kg.
- Using the circle tool draw a circle of radius 0.2 m and set its mass to 100 kg.
- Attach the circle to the 1m line on the rod using the "fixate tool".
- pivot the rod at the 3m mark using the "axle tool".
- Test to make sure everything moves freely by running the animation then giving it a push with the "drag tool".
- Reset the simulation so the rod is horizontal again
Applying the Torque
In the lab we apply a torque using hanging masses and pulleys but in the simulation we will use a rocket.
- Attach a thruster to the 4 m mark on the rod. Position it so that it points vertically (to adjust the angle finely move the cursor outside the circle)
- Set the force to 10 N by double clicking the thruster.
- Tick "thruster follows geometry rotation" so the rocket rotates with the rod.
- Use your knowledge of rotational mechanics to calculate the angular acceleration of the body.
- Double click the rod and from the "plot" options plot a graph of angular velocity against time, from the gradient find the angular acceleration and compare it to your calculation. If not the same check your calculations and adjust the simulation so that the values agree.
- Reset the simulation then run it so that the rod rotates 180°.
- Calculate the work done by the Torque.
- Use the angular velocity vs time plot to find the final angular velocity.
- Calculate the KE of the body and compare your answer with the work done.
- Adjust the position of the Torque and circle and repeat.
- Try other more complicated bodies.