A bucket is whirled in a vertical circle with a rope tied to it.
The bucket has a mass of 3 kilograms.
A uniform meter stick of mass 1 kilogram is hanging from a thread.
If the distance between two point particles is doubled, then the force between them decreases by a factor of 4 and increases by a factor of 2.
The mass of the dwarf planet is 1/600 and the distance from Earth is 1/15.
You are looking at a planet that is in the middle of the sun.
A robot probe lands.
The diameter of the planet is 8 x 106 m.
You can write your answer in both m/s2 and g's.
The Earth has a mass of 6 x 1000 km and is in a constant circle around the Sun.
An amusement park ride consists of a large cylinder that rotates around its central axis as passengers stand against the inner wall of the cylinder.
The passengers feel pinned against the wall of the cylinder as it rotates.
Don't include friction.
The centripetal force is given by and the centripetal acceleration is given by.
A force that makes an object rotate is called Torque.
Torques can be clockwise or counterclockwise.
Universal gravitation can be linked up with circular motion.
Robert Hooke was a British physicist who helped pave the way for simple motion.
Newton's laws of static equilibrium made it possible to show a relationship between stress and strain.
Hooke's Law is one of the laws he developed after building upon these.
The concise mathematical relationship of a spring was discovered by Hooke.
In this section, we will focus on periodic motion that is simple and easy to understand.
There is a fixed block on the left side of the wall.
The spring is said to be in its equilibrium position when it is not stretched or compressed.
The net force on the block is zero when the block is in equilibrium.
There is a spring at rest.
When we pull the block to the right, it will experience a force pulling back toward equilibrium.
The block will once again be pushed toward the equilibrium position by a force.
The block passes through the equilibrium position again, but this time it is traveling to the right.
This back-and-forth motion will continue indefinitely if this is taking place in ideal conditions, and the block will oscillate from these positions in the same amount of time.
The block at the end of this spring has a physical example of SHM.
Since the block is decelerating, there must be some force behind it.
The spring exerts a force on the block that is proportional to its displacement from its equilibrium point.
This is called Hooke's Law.
Hooke's Law states that the force is a restoring force.
The force wants to return the object to its equilibrium position.
The force was to the right when the block was on the left, and it was to the left when the block was on the right.
In all cases of the extreme left or right, the spring tends to return to its original position.
The force helps to maintain the movement of the body.
We would have to exert a lot of force to keep the spring in this state.
The number tells us how far away from equilibrium the block will travel.
The block's motion can be described in terms of energy transfers.
The more work you have to do, the more potential energy that's stored.
The block's energy transfers can be described as follows.
The elastic energy of the system increases when you pull the block out.
The block moves when the potential energy turns into energy.
All the energy is in motion.
As the block continues through equilibrium, it transforms the spring's energy into elastic potential energy.
This method can only calculate the maximum velocity in a spring.
The AP physics 1 exam won't ask you to calculate other velocities at other points because it's not uniform accelerated motion.
The result is a oscillations of 8.0 cm.
Determine the total energy and speed of the block when it's less than 4 cm from equilibrium.
The total energy is the sum of the two energies.
The block is at rest.
The block has an initial speed of 2.0 m/s.
When the spring's potential energy has been transformed into the block's initial energy, it will come to rest.
The number of cycles that can be completed in a given time interval is a way of indicating the rapidity of the oscillations.
You can always get the frequencies if you have the period.
The period and Frequency are inverses of each other.
A block on the end of a spring moves from maximum spring stretch to maximum spring compression in 0.25 s.
The time required for one full cycle is defined as the period.
It's only half a cycle when you move from one end of the region to the other.
2 s is 1/(0.5 s)
A student is observing a block.
Determine its frequencies in hertz and seconds.
The force constant of the spring and the mass of the block are two of the defining properties of the spring-block oscillator.
Let's look at the equations.
If we had a small mass on a very stiff spring, we would expect that the strong spring would cause the mass to change shape quickly.
A block is attached to a spring and set into motion.
A student is doing an experiment.
In the first trial, the amplitude is 3.0 cm, while in the second trial it is 6.0 cm.
The values of the period, Frequency, and maximum speed of the block can be compared.
The period and Frequency are not dependent on the amplitude.
The period and frequencies in the second trial will be the same as in the first trial, because the same spring and block were used.
The maximum speed of the block will be greater in the second trial.
The second system has more energy to convert to kinetic when the block is passing through equilibrium.
The force constant of a single spring is the same force on the block as the pair of springs shown in each case.
The second spring is stretched.
The simple motion follows this cycle.
We've seen a block sliding back and forth on a table, but it could also move vertically.
The only difference would be that gravity would cause the block to move downward, to an equilibrium position at which the spring would not be at its natural length.
There is a spring hanging from a support.
The upward force of the spring is balanced by the downward force of gravity as the block is in equilibrium.
Our net force is zero since it is not moving up or down.
The vertical spring can be treated the same as the horizontal spring at this point.
If a question asks about the total length of the spring at a given moment, you don't need to worry about this.
The block is pulled down a distance of 2.0 cm after it comes to rest.
When the block is at the lowest position in its cycle, the spring is stretched a maximum of 7 cm, and a minimum of 5 cm when the block is at its highest position.
The simple pendulum has many of the same features as the spring-block oscillator, but the displacement of the pendulum is measured by the angle that it makes with the vertical, rather than by its linear distance from the equilibrium position.
The equilibrium position has zero displacement.
The pendulum's energy and speed are maximized when it passes through the equilibrium position.
There is one important difference despite the similarities.
There is a restoring force that is proportional to the displacement.
The motion of a simple pendulum is not simple.
The periods and frequencies are not dependent on the mass of the weight.