Circular Applications
In this lesson we will explore a number of applications of circular motion, and where appropriate, examine the applications quantitatively.
We will look at the conical pendulum, banked curves, rollercoaster and some other amusement park rides
We will look at the conical pendulum, banked curves, rollercoaster and some other amusement park rides
The conical pendulum and banked curves
The conical pendulum and banking both are more complex examples of centripetal motion. This video examines these situations. An understanding of the basics of circular motion, normal and friction is assumed.
A summary on the principles of banked curves, useful for review
Interactive
This is a useful interactive that examines the conical pendulum
This is a useful interactive that examines the conical pendulum
Sample Problems
We are now ready to try some sample problems
Below is are sample problems with a video that explain how to solve them. It is suggested you try the problems beforehand, as this actually aids understanding, even if you are unsure if you are correct.
We are now ready to try some sample problems
Below is are sample problems with a video that explain how to solve them. It is suggested you try the problems beforehand, as this actually aids understanding, even if you are unsure if you are correct.
Some more problems for you to try
1. A car (m = 1500kg) is travelling around a circular corner that has a radius of 20m. If the coefficient of the road surface to the tyres is 0.8.
a. What is the frictional force, the car experience in the turn?
b. What is the maximum speed that car can travel around the curve?
c. As it goes into the turn, it encounters a wet section that reduces μ to 0.5. Explain what happens to the car?
2. You are in a roller coaster that is approaching a circular loop, that has a diameter. Of 60m. You forgot to buckle in. What speed must you enter to to ensure you don't fall out (HINT: Apart from circular motion, you also need to consider conservation of energy, and assume negligible loss of energy due to friction)
3. A pendulum is rotating with a frequency of 1.5 Hz with a radius of 5 cm, as shown to the right. What is the angle?
4. A 70 tonne 737 makes a banking turn to come into land. If the radius is 2km and its speed is 300km/h a. What will be its banking angle? b. What would be the force it experiences to painting this turn (ie the Normal)
1. A car (m = 1500kg) is travelling around a circular corner that has a radius of 20m. If the coefficient of the road surface to the tyres is 0.8.
a. What is the frictional force, the car experience in the turn?
b. What is the maximum speed that car can travel around the curve?
c. As it goes into the turn, it encounters a wet section that reduces μ to 0.5. Explain what happens to the car?
2. You are in a roller coaster that is approaching a circular loop, that has a diameter. Of 60m. You forgot to buckle in. What speed must you enter to to ensure you don't fall out (HINT: Apart from circular motion, you also need to consider conservation of energy, and assume negligible loss of energy due to friction)
3. A pendulum is rotating with a frequency of 1.5 Hz with a radius of 5 cm, as shown to the right. What is the angle?
4. A 70 tonne 737 makes a banking turn to come into land. If the radius is 2km and its speed is 300km/h a. What will be its banking angle? b. What would be the force it experiences to painting this turn (ie the Normal)
Rollercoasters and looped tracks
Roller coasters provide a great way to examine physics concepts: everything from forces, momentum, and energy - from both a linear perspective and rotational.
This covers these concepts and is here since loops are examined.
Many motion graph analysis video examine simplistic examples where velocity is constant or acceleration is constant.
In this video I analyse a well known toy which has more complex motion, and I apply the same skills taught to analyse its graph. This video helps students consolidate their understanding of motion graphs, as well as review concepts such as friction, energy and forces.
In this video I analyse a well known toy which has more complex motion, and I apply the same skills taught to analyse its graph. This video helps students consolidate their understanding of motion graphs, as well as review concepts such as friction, energy and forces.