find out an expression for centripetal acceleration
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To derive this equation one requires some elementary knowledge of vectors.
First off, v^2/r is the acceleration of the body moving in the circular path.
To get force we are required to multiply it with mass m kg.
Then F=m*(v^2/r)
Acceleration is the rate of change of velocity with time, velocity being a vector quantity is described by magnitude as well as direction.
Interestingly in circular motion the magnitude doesn't change but the direction does.
Now consider a circular motion as shown.
Let us suppose the object was at point B and had velocity V1 as shown,
and after certain small time dt it is at point c having velocity V2.( Note that velocity doesn't change in magnitude but in direction which is tangent to circle)
By vector addition V2=V1 + ΔV, now for very small angle between b and c, we can approximate V1=V2=V(some magnitude).
Also as per figure dV can be taken as an arc subtended between V1 and V2 which are taken equal.
Hence ΔV= V*dɵ( rule or arc length l= r*ɵ)
Now acceleration a eqauls change of velocity per unit time.
So a = ΔV/dt = (V*dɵ)/dt
Now dɵ/dt = angular velocity= ω =V/r. Substitute this in above equation to get
a= (V^2)/r
●MARK BRAINLIEST..●
First off, v^2/r is the acceleration of the body moving in the circular path.
To get force we are required to multiply it with mass m kg.
Then F=m*(v^2/r)
Acceleration is the rate of change of velocity with time, velocity being a vector quantity is described by magnitude as well as direction.
Interestingly in circular motion the magnitude doesn't change but the direction does.
Now consider a circular motion as shown.
Let us suppose the object was at point B and had velocity V1 as shown,
and after certain small time dt it is at point c having velocity V2.( Note that velocity doesn't change in magnitude but in direction which is tangent to circle)
By vector addition V2=V1 + ΔV, now for very small angle between b and c, we can approximate V1=V2=V(some magnitude).
Also as per figure dV can be taken as an arc subtended between V1 and V2 which are taken equal.
Hence ΔV= V*dɵ( rule or arc length l= r*ɵ)
Now acceleration a eqauls change of velocity per unit time.
So a = ΔV/dt = (V*dɵ)/dt
Now dɵ/dt = angular velocity= ω =V/r. Substitute this in above equation to get
a= (V^2)/r
●MARK BRAINLIEST..●
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