0.27 Phy1240: circular motion -- speed and velocity  (Page 3/3)

where

• s1 through s4 represent the four different speeds
• r1 through r4 represent the radii of the four circles

Speed is proportional to radius

As you can see, the average speed for each rider is directly proportional to the radius of the circle on which that rider is traveling. Doubling the radius doubles the average speed. Ifthere were a horse located 5 meters from the center of the carousel, the average speed for that horse would be only half of your average speed at 10 meters, or 1m/s.

Velocity

Just because you are traveling at a constant speed (during a portion of the ride anyway), doesn't mean that you are traveling at a constant velocity. Youlearned in an earlier module that an object in motion tends to remain in motion in a straight line unless a force is applied to cause the object to changedirection.

You are constantly changing direction

When you are riding on the carousel, you are constantly changing direction. Otherwise you would travel in a straight line instead of traveling in a circle.

A force is required to cause you to continually change direction and to travel in a circle. That forceis exerted on your body by your grasp on the horse on which you are sitting.

Goodbye horse and rider

If the brackets that attach your horse to the carousel were to break, you wouldcontinue to travel in a straight line at that point, leaving the carousel behind.

A tangential velocity vector

At any instant in time, the direction of your velocity vector is a direction that is tangent to the circle on which you are traveling. Stated differently,the direction of your velocity vector is along a line that is perpendicular to a line that extends from your center of mass to the center of the circle. (A tangent line is a line that touches a circle at one point but does not intersect it.)If you sit very straight on the horse and face straight ahead, you will be facing the direction of your velocity vector.

Summary

An object moving in uniform circular motion is moving around the perimeter of the circle with a constant speed. Although the speed of the object is constant, the object's velocity isconstantly changing.

The object's velocity vector has a constant magnitude but a changing direction. At any instant in time, the direction of the velocity vector is tangent to the circle.As the object travels along the circular path, during one full rotation (cycle) around the center, the tangent line is always pointing in a new direction.During each cycle, the velocity vector points in the same (infinite) set of directions.

A force must be exerted on an object to cause it to travel along a circular path instead of traveling in a straight line. As you will learn in afuture module, this force is called the centripetal (center seeking) force.

A thought experiment

Assume that you attach one end of a garden hose to a faucet and then arrange the hose in a circle on the ground. When you turn the water on, will the waterexit the hose and continue moving in a circular path, or will it move in a straight line (ignoring the effects of gravity, air resistance, etc.)?

You may already know from experience that when the water exits the hose, it moves in a straight line. While the water was inside the hose, it moved in acircular path due to the force exerted on the water molecules by the inside surface of the hose.

When the water exits the hose, that force will no longer be applied to the water molecules. According to Newton, the water will continue in motionat a constant velocity, meaning that the direction of the velocity vector for the water molecules will not change.

Resources

I will publish a module containing consolidated links to resources on my Connexions web page and will update and add to the list as additional modulesin this collection are published.

Miscellaneous

This section contains a variety of miscellaneous information.

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