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The acceleration of an object going at a constant speed around a circle is

a = v^2 / r ,

and the acceleration is directed toward the center of the circle

Therefore:

• a = (30 cm/s)^2 / 20cm = 45 cm/s^2

Net force = mass * acceleration, and the centripetal force is the net force.  Thus

• centripetal force = mass * centripetal acceleration.

The object's mass is 110g = .110kg, and 45 cm/s^2 = .45 m/s^2 so

• F_cent = m * a_Cent = .110kg * .45 m/s^2 = .0495 kg * m/ s^2 = .0495 N

Since net force = mass * acceleration, an acceleration toward the center implies a net force toward the center.

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Some questions and answers related to this problem:

However in query 24 I read about the centripetal acceleration being equal to the acceleration of gravity, which would simply be 9.8 m/s^2 or 980cm/s^2

This is not so in this problem.  It is so in a specific special case of a mass swinging in a vertical circle, provided the string goes slack for an instant at the very top of the circle. At that instant there is no tension in the string and only gravity acts on the mass. Since the mass remains in the circular path, its centripetal acceleration at that instant comes only from gravity and is equal to the acceleration of gravity.

In QA 24 I also learned that the acceleration is directed toward the center of the circle, but then my notes say that the centripetal force is also directed toward the center of the circle.

Since centripetal force = mass * centripetal acceleration (and since mass is a positive quantity), the force and acceleration must be in the same direction.

In query 24 I figured that the motion of the object is perpendicular to the force maintaining its circular motion. Either way I’m not sure how you would determine the direction of a ball traveling in a circle. I might say that it is 360 degrees. But if it is perpendicular to the force then I might just assign it to be along the x axis and the force to be along the y axis.

The centripetal force is perpendicular to the velocity of an object moving on a circle:

• The direction of the velocity vector is tangent to the circle, while the direction of the acceleration, and therefore the force, is toward the center. 

• A vector from a point on the circle toward the center is opposite to the radial line from the center to the point, and both vectors are perpendicular to the tangent line.

This applies at any point. So if the ball happens to be on the y axis then the tangent vector and therefore the velocity is in the x direction, while the acceleration is in the y direction.

The magnitude is v^2/r = 900/20 = 45 cm/s/s or .45 m/s/s and I believe I remember reading the acceleration is always directed towards the center of the circle.

The acceleration is toward the center of the circle is this case, and it is so any time an object moves along a circle with constant velocity.

Any time an object moves along a circle, whether velocity is constant or not, centripetal acceleration is v^2 / r and is toward the center (that's what 'centripetal' means); since the direction of motion along the circle is always perpendicular to its velocity, the centripetal acceleration is perpendicular to the velocity.

If the object is changing speed there is an additional component of acceleration in the direction of motion.

I assume that the .05N of force must be maintained to keep it moving.

It doesn't take any force to keep something moving; zero net force implies constant velocity, meaning constant speed and direction.

However this object keeps changing its direction as it goes around the circle, and this does take a net force, equal to the one you've calculated.

This force won't change the object's speed, only its direction. There might be other forces (air resistance to slow it, an engine to speed it up) that do change the object's speed, but the centripetal force remains directed toward the center, perpendicular to the object's velocity, and therefore does no work on the object.