A particle is moving along the circular path with a speed v and its speed ingreases by g in one second
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We have a case of accelerated circular motion. Given rate of change of velocity
dvdt=g=→at
Assuming u be initial velocity, velocity v after time t of the particle is given by the kinematic expression
v=u+gt
Tangential acceleration →at is parallel to velocity of the particle.
Radial acceleration is given by
→ar=rω2=v2r=(u+gt)2r
here we see that ω=vr is also changing with time due to accelerated motion.
As both accelerations are orthogonal to each other, net acceleration of the particle can be found from the expression
an=√∣∣→at∣∣2+∣∣→ar∣∣2
an= ⎷g2+((u+gt)2r)2
an=√g2+(u+gt)4r2
dvdt=g=→at
Assuming u be initial velocity, velocity v after time t of the particle is given by the kinematic expression
v=u+gt
Tangential acceleration →at is parallel to velocity of the particle.
Radial acceleration is given by
→ar=rω2=v2r=(u+gt)2r
here we see that ω=vr is also changing with time due to accelerated motion.
As both accelerations are orthogonal to each other, net acceleration of the particle can be found from the expression
an=√∣∣→at∣∣2+∣∣→ar∣∣2
an= ⎷g2+((u+gt)2r)2
an=√g2+(u+gt)4r2
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