why is the force needed to keep a body moving over a circular path
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Because motion (velocity) is a vector quantity - it has direction and magnitude; in this case speed is the magnitude of the velocity.
But the body is moving in a circle; the direction of that velocity is changing. So the speed might be the same, but the velocity vector is changing.
About now you should review your mathematical study of vectors.
Acceleration by definition is also a vector (the first differential of velocity with time or in simpler words, how much the velocity is changing with time). Note, acceleration is not just about changing speed, rather it determines how much the velocity vector is changing.
Since the velocity of a body in circular motion is changing there must be a non-zero acceleration causing that change in velocity.
And if the body has mass, there must be a Force that causes this acceleration, as per Newton’s law of motion F=ma
Do the vector math, and you find there must be a Force acting always in direction towards the centre of the circle of magnitude F=m*s*s/r where s is speed, r is radius, m is body mass. This is the only solution that causes a body of mass m to move in circular motion at constant speed.
You should at this point be able to visualise that if this force is not present, the body would just carry on in a straight line tangent to the circle; an object moving at constant speed in a straight line has an unchanging velocity (both its magnitude and direction are unchanging) so no acceleration, so no force acting on it.
If you have difficulty with understanding this, you need to go back and review what a vector is, and the mathematics associated with it. The key point being speed is only part of motion, the direction of that speed being the other part, and the two parts are expressed very nicely in the form of a vector called velocity.
hope this answer is useful to u if helps plz mark it as brain list
But the body is moving in a circle; the direction of that velocity is changing. So the speed might be the same, but the velocity vector is changing.
About now you should review your mathematical study of vectors.
Acceleration by definition is also a vector (the first differential of velocity with time or in simpler words, how much the velocity is changing with time). Note, acceleration is not just about changing speed, rather it determines how much the velocity vector is changing.
Since the velocity of a body in circular motion is changing there must be a non-zero acceleration causing that change in velocity.
And if the body has mass, there must be a Force that causes this acceleration, as per Newton’s law of motion F=ma
Do the vector math, and you find there must be a Force acting always in direction towards the centre of the circle of magnitude F=m*s*s/r where s is speed, r is radius, m is body mass. This is the only solution that causes a body of mass m to move in circular motion at constant speed.
You should at this point be able to visualise that if this force is not present, the body would just carry on in a straight line tangent to the circle; an object moving at constant speed in a straight line has an unchanging velocity (both its magnitude and direction are unchanging) so no acceleration, so no force acting on it.
If you have difficulty with understanding this, you need to go back and review what a vector is, and the mathematics associated with it. The key point being speed is only part of motion, the direction of that speed being the other part, and the two parts are expressed very nicely in the form of a vector called velocity.
hope this answer is useful to u if helps plz mark it as brain list
Tejaswini415:
plz mark it as brain list friend
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