Question

A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.00 m, 4.00 m) with a velocity of 5.00 m/s2 and an acceleration of +12.5 m/s2.What are the (a) x and (b) y coordinates of the center of the circular path?

Answer 1

When traveling in circular motion with constant speed,

the instantaneous acceleration vector necessarily points toward the center.

Thus, the center is “straight up” from the cited point.

(a) Since the center is “straight up” from (4.00 m, 4.00 m),

the x coordinate of the center is 4.00m.

(b) To find out “how far up” we need to know the radius. Using a=

r

v

2

​

we find

r=

a

v

2

​

=

12.5m/s

2

(5.00m/s)

2

​

=2.00m.