To determine the acceleration of a particle in uniform circular motion, we start with the equation of the circle:
(x−2)2+y2=25This equation represents a circle with its center at
(2,0) and a radius
r of 5 meters, derived from:
r2=25⇒r=5 In uniform circular motion, the centripetal acceleration
ac is given by the formula:
ac=‌Substituting the given speed
v=2m∕ s and the radius
r=5m :
ac=‌=‌=0.8m∕ s2 When the particle is at the lowest
y-coordinate, it is at the point
(2,−5), assuming downward is along the negative
y-axis. At this point, the acceleration vector, which is directed towards the center of the circle, points horizontally to the right towards the center
(2,0). Therefore, the acceleration is entirely in the
direction:
=0.8m∕ s2