Understanding Classical Mechanics: Acceleration

In summary, the conversation discusses the concept of determining acceleration in classical mechanics by defining coordinates and velocities. The equations of motion with given coordinates and velocities allow for the calculation of acceleration, assuming that the generalized force only depends on these two variables. This is a commonly accepted assumption in classical mechanics.
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I'm reading once again through Landau-Lifchitz and I am stuck on the first page! I can't wrap my head around why we only need to define the coordinates and velocities to determine the acceleration? Surely if we only know those two in a single point in time, that's not enough to determine an acceleration? What am I missing here? Thanks!
 
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From the equations of motion with given ##q## and ##\dot{q}## you get ##\ddot{q}##. Of course you need the assumption that the (generalized) force depends only on ##q## and ##\dot{q}## as usual in classical mechanics.
 
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FAQ: Understanding Classical Mechanics: Acceleration

What is acceleration?

Acceleration is the rate of change of an object's velocity over time. It is a vector quantity, meaning it has both magnitude (size) and direction.

How is acceleration related to force?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be represented by the equation F=ma, where F is force, m is mass, and a is acceleration.

What is the difference between average and instantaneous acceleration?

Average acceleration is the change in velocity over a specific period of time, while instantaneous acceleration is the acceleration at a specific moment in time. Average acceleration can be calculated by dividing the change in velocity by the change in time, while instantaneous acceleration can be found by taking the derivative of the velocity with respect to time.

How does acceleration affect an object's motion?

Acceleration can cause an object to speed up, slow down, or change direction. If an object is accelerating in the same direction as its velocity, it will speed up. If it is accelerating in the opposite direction, it will slow down. If the acceleration is perpendicular to the velocity, the object will change direction.

What are some real-life examples of acceleration?

Some common examples of acceleration in everyday life include a car speeding up or slowing down, a ball falling towards the ground due to gravity, and a person jumping off a diving board. Other examples include a rocket launching into space, a cyclist pedaling faster to increase their speed, and a roller coaster going around a loop.

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