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Objects that move at a constant velocity
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What is the acceleration of an object that moves at a constant velocity?
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While I certainly respect buildersmate's consistently accurate and helpful answers, the problem of intutitveness arises when one definition of a term collides with another.
Newton clearly demonstrates that a body can have nonzero acceleration while moving at constant speed. This was shown by his principal of a cannon being fired from a high mountain with enough velocity for the projectile to circle the Earth at a constant speed. The projectile's velocity is changing constantly, because velocity includes direction. Newton predicted that when two measurements of the velocity vectors are taken one second apart, and a graph line is plotted from the position of vector a to the new vector b (one second later) This graph line can be measured, which measurement yields the actual vector change although the projectile has been in constant velocity at all times. One source, for example, states explicitly that "... When we understand acceleration as the rate of change of velocity, which is a vector, a body moving at a steady speed around a circle is accelerating towards the center all the time, although it never gets any closer to it."
We see this principal in the orbit of all satellites and the International Space Station....
Newton clearly demonstrates that a body can have nonzero acceleration while moving at constant speed. This was shown by his principal of a cannon being fired from a high mountain with enough velocity for the projectile to circle the Earth at a constant speed. The projectile's velocity is changing constantly, because velocity includes direction. Newton predicted that when two measurements of the velocity vectors are taken one second apart, and a graph line is plotted from the position of vector a to the new vector b (one second later) This graph line can be measured, which measurement yields the actual vector change although the projectile has been in constant velocity at all times. One source, for example, states explicitly that "... When we understand acceleration as the rate of change of velocity, which is a vector, a body moving at a steady speed around a circle is accelerating towards the center all the time, although it never gets any closer to it."
We see this principal in the orbit of all satellites and the International Space Station....
Ignore your example of orbiting a planet any body undergoing circular motion doesn't have constant velocity, it may have a constant linear speed but not constant velocity and the question specifically stated constant velocity. A constant velocity is just that, a constant magnitude and direction, hence no acceleration. Any body moving at constant velocity has no net force acting on it, a body with constant speed can have a force acting on them, most commonly bodies moving in circular motion with a force acting towards the centre of motion.
I agree. It's crucial to distinguish between speed and velocity. You can go round in a circle at a constant speed but because you're direction is changing all the time then your acceleration is NOT zero.
Don't forget also that for there to be an acceleration there must be a force acting on the body. When a body is going round in a circle at constant speed the force is keeping it in a circle, otherwise it would move in a straight line.
No force , no acceleration.
Don't forget also that for there to be an acceleration there must be a force acting on the body. When a body is going round in a circle at constant speed the force is keeping it in a circle, otherwise it would move in a straight line.
No force , no acceleration.
Be that as it may, Kepler clearly demonstrated the validity of Newton's Laws, especially "... that Uniform Circular Motion applies to all objects that maintain a constant velocity magnitude but constantly change velocity direction. Since the direction is always changing, a centripetal acceleration must be present. Centripetal acceleration is the acceleration caused by centripetal force and directed toward the center of the circle radially.
Mathematically, a = v^2/r, where a is the centripetal acceleration, v is the velocity (magnitude only), and r is the radius (the distance of the object from the center of the circle. By using the previous equation for acceleration, the centripetal force on an object equals the mass times the velocity squared divided by the radius. Mathematically, F = mv^2/r, where F is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius. Centripetal force is not a true force; therefore, it is called a psuedoforce. Though the direction of the velocity changes, the magnitude of the velocity is constant for an object in uniform circular motion. The acceleration of an object in circular motion is equal to v^2/r, the acceleration according to uniform gravitation is equal to Gm/r^2, therefore Gm/r^2 = v^2/r, or v = sqrt (Gm/r), where G is the constant for gravitation, m is the mass of the object, r is the radius, and v is the velocity�s magnitude. This equation only applies to satellites and celestial bodies affected by gravity. (Source: NASA -Orbital Mechanics).
There is no linear acceleration along an orbital flight path, but only acceleration in the direction of its motion. This acceleration is centripetal acceleration, because the direction of travel is always inwards towards the center of the circular orbit.
Mathematically, a = v^2/r, where a is the centripetal acceleration, v is the velocity (magnitude only), and r is the radius (the distance of the object from the center of the circle. By using the previous equation for acceleration, the centripetal force on an object equals the mass times the velocity squared divided by the radius. Mathematically, F = mv^2/r, where F is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius. Centripetal force is not a true force; therefore, it is called a psuedoforce. Though the direction of the velocity changes, the magnitude of the velocity is constant for an object in uniform circular motion. The acceleration of an object in circular motion is equal to v^2/r, the acceleration according to uniform gravitation is equal to Gm/r^2, therefore Gm/r^2 = v^2/r, or v = sqrt (Gm/r), where G is the constant for gravitation, m is the mass of the object, r is the radius, and v is the velocity�s magnitude. This equation only applies to satellites and celestial bodies affected by gravity. (Source: NASA -Orbital Mechanics).
There is no linear acceleration along an orbital flight path, but only acceleration in the direction of its motion. This acceleration is centripetal acceleration, because the direction of travel is always inwards towards the center of the circular orbit.
Yes we've all agreed on that, bodies in circular motion have a force acting on them (and centripetal force is real) but the question was about an object with constant velocity, NOT constant magnitude of velocity. For bodies with constant velocity there is no acceleration, bodies in circular motion are continuously accelerating.
Answer the question Clanad, not copy an essay about circular motion.
A force is equal to change in momentum per unit time, the change in momentum is a vector and does not draw any distinction between so called linear acceleration and angular acceleration.
Answer the question Clanad, not copy an essay about circular motion.
A force is equal to change in momentum per unit time, the change in momentum is a vector and does not draw any distinction between so called linear acceleration and angular acceleration.
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