Is an object moving at a constant speed in a circle accelerating? When an object is moving at a constant speed in a circle it is accelerating. Since we know that slowing down, speeding up, and changing direction are the three ways to accelerate we can prove this. Looking at figure (1-a) might help you further understand this.

Figure (1-a) This picture shows an object moving at a constant speed in a circle. Since the object is constantly changing direction the object is accelerating. What causes the object to change direction?

The force causing the object to change direction is called the centripetal force. The centripetal force always pulls towards the center or inwards. There are many forces that can provide the centripetal force. Tension, friction, and gravity are just a few of these. When a car turns a corner the friction pulls inwards allowing the car to make the turn. If the centripetal force disappeared while an object was moving around the circle, the object would continue to move in a straight-line tangent to the circle.

Centripetal acceleration is equal to the velocity squared divided by the radius.	Centripetal force is equal to the mass multiplied by the velocity squared divided by the radius.

Circular Motion Example Problem

Universal Gravitation:

It is important to understand that any two masses; anywhere will attract one another. If you held up to bowling balls 2 feet apart the bowling balls will attract each. The attraction between the bowling balls is so small you can not even feel it. Just like the bowling balls attract each other the earth and the sun attract each other. Then why doesn't the sun fly into the moon? Well if you take what you learned from circular motion you know that gravity can be a centripetal force. We also know that the centripetal force always pulls inwards or towards the center. This force causes the earth to circle the sun.

Force is equal to the universal constant multiplied by the mass of object 1 by the mass of object divided by the radius squared.

Universal Gravitation Example Problem

Planetary Data
Name	Average radius (m)	Mass (kg)	Mean distance from sun (m)
Sun	696.0 x 10(6)	1.991 x 10(30)	-------
Earth	6.3713 x 10(6)	5.979 x 10(24)	1.4957 x 10(11)
Mercury	2.43 x 10(6)	3.2 x 10(23)	5.80 x 10(10)
Venus	6.073 x 10(6)	4.88 x 10(24)	1.081 x 10(11)
Mars	3.38 x 10(6)	6.42 x 10(23)	2.278 x 10(11)
Jupiter	69.8 x 10(6)	1.901 x 10(27)	7.781 x 10(11)
Saturn	58.2 x 10(6)	5.68 x 10(25)	1.427 x 10(12)
Uranus	23.5 x 10(6)	8.68 x 10(25)	2.870 x 10(12)
Neptune	22.7 x 10(6)	1.03 x 10(26)	4.500 x 10(12)
Pluto	1.15 x 10(6)	1.2 x 10(22)	5.9 x 10(12)

Posted 12/12/00