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Lab 4: Uniform Circular Motion
(Interactive Activity)
Name: LakshmiPrasanthi Malepati
Objective:
The purpose of this activity is to explore the characteristics of the motion of an object in a circle at a constant speed.
Theory:
Newton's first law of motion tells us that a body will remain at rest or moving with constant speed in a straight line unless acted on by an unbalanced force. If a force, not along the path of motion, acts on such a body only for an instant, the body will be deflected but will continue in a straight line at an angle from its former path. On the other hand, if the force acts continuously on a body at right angles to the path of motion, the object will move along a circular path.
If a body is moving at uniform speed in a circle, it is said to have uniform circular motion. Even though the speed is constant, the velocity is continually changing. The direction of the motion is continually changing, so the body is accelerating. The acceleration is always directed toward the center of the circle with a magnitude given by
a c =^ v^
2
r
Equation 1
where v is the linear speed of the body and r is the radius of the circle. Since the acceleration is
directed towards the center of the circle, it is called Centripetal Acceleration. The term centripetal means "center-seeking."
A force is necessary to produce this acceleration. This is called centripetal force because it, too, is always directed toward the center, as shown in Figure I.
The magnitude of this centripetal force is determined by straightforward application of Newton’s Second Law:
Since F net = ma then F c = m a c.
So,
F c = m v^
2
r
Equation 2
where Fc is the centripetal force, m is the mass, and v and r are the same as before. The object's motion results from competition between its inertia, which tends to make it move tangent to the circle, and the centripetal force, which coaxes it out of its straight-line motion. The net result is the circular path. It may seem that a force, often called the centrifugal force, is pulling the object away from the circle, but in fact no such force acts on the object.
We can also express the centripetal force in terms of the angular speed, since
v = rω Equation 3
and
ω = 2 πf Equation 4
In these relations, v is the linear speed, r is the radius of the circle, ω is the angular speed in
radians/ seconds, and f is the frequency in revolutions/second or hertz. Using these relations, it
may be concluded that since.
F c = m v^
2
r =
m ( rω )^2
r =^ mr^ ω^
2
Also, since ω = 2 πf , then
F (^) c = mr ω 2 = 4 π 2 f 2 m Equation 5
This relation may be used to calculate the centripetal force for an object of mass ( m ) traveling in
a circle of radius r with frequency ( f ).
- In the diagram at the right, a variety of positions about a circle are shown. Draw the velocity vector at
the various positions; direct the ⃗ v arrows in the
proper direction and label them as ⃗ v. Draw the
acceleration vector at the various positions; direct the
⃗ a arrows in the proper direction and label them as ⃗ a.
This acceleration is called centripetal acceleration.
- In the above diagram, uniform circular motion, the velocity vector is always tangent to the circular path while the acceleration vector always points toward the center of the circle, causing the object to continuously change direction without changing speed. .
- Describe the relationship between the direction of the velocity vector and the direction of the acceleration for a body moving in a circle at constant speed. -The velocity vector is always perpendicular to the acceleration vector. Velocity is tangent to the circle, while acceleration points toward the center.
- A Puzzling Question to Think About : If an object is in uniform circular motion, then it is accelerating towards the center of the circle; yet the object never gets any closer to the center of the circle. It maintains a circular path at a constant radius from the circle's center. Suggest a reason as to how this can be. How can an object accelerate towards the center without ever getting any closer to the center?
-The acceleration changes only the direction of motion, not the distance from the center. Since the acceleration is always perpendicular to velocity, it bends the path into a circle instead of pulling the object inward.
- A Thought Experiment : Suppose that an object is moving in a clockwise circle (or at least trying to move in a circle).
- Suppose that at point A the object traveled in a straight line at constant speed towards B'. In what direction must a force be applied to force the object back towards B? Draw an arrow on the diagram in the direction of the required force.
- If an object moving along a circular path at point A begins to drift in a straight line toward point B' (outside the circle path), a force must be applied toward point B (the next point on the circular path) to redirect it back to the circle. The direction of this required force would be inward, towards the center of the circular path. The red arrow pointing inward is for this section of the experiment.
- Repeat the above procedure for an object moving from C to D'. In what direction must a force be applied for the object to move back to point D along the path of the circle? Draw an arrow on the diagram. - If the object moves from C in a straight line toward D' (deviating from the circular path), a force directed toward D (the point on the circle where it would naturally be if continuing in a circle) must be applied. This force would also point inward, pulling the object back onto the circular path. The blue-ish arrow pointing inward from D is for this section of the experiment.
- If the acceleration of the body is towards the center, what is the direction of the unbalanced force? Using a complete sentence, describe the direction of the net force that causes the body to travel in a circle at constant speed.
- - The acceleration of an object in uniform circular motion is always directed toward the center of the circle; the net force must also point inward toward the center. This centripetal force acts perpendicularly to the object’s velocity,
Conclusion:
Write a conclusion to this activity in which you completely and intelligently describe the characteristics of an object that is traveling in uniform circular motion. Give attention to the quantities speed, velocity, acceleration, and net force.
-In uniform circular motion, an object moves at constant speed but its velocity continuously changes because its direction changes at every point along the path. This change in direction means the object is accelerating even though its speed remains the same. The acceleration, called centripetal acceleration, always points toward the center of the circle and is produced by a centripetal force. The velocity is tangent to the path while acceleration and force are inward. The magnitude of acceleration depends on the square of speed and inversely on the radius. This explains how objects like planets, cars turning, and satellites maintain circular motion.
Grading Rubric for Lab 4: Uniform Circular Motion
As you know from the syllabus for this course, each lab you complete is worth 20 points. This rubric is provided so that you can see where the 20 points come from and so that you can be sure to include everything listed so that you maximize your points on this lab assignment. I will follow this rubric when grading your Lab 4. If you do not complete or do not include a part listed on this rubric, then those points will be automatically deducted from your overall 20-point score.
Good Luck!
Question given in step # 6 2 points
Question given in step # 7 1 point
Diagram given in step # 8 2 points
Question given in step # 9 1 point
Question given in step # 10 2 points
Diagram given in step # 11 2 points
Question given in step # 11 2 points
Question given in step # 12 1 point
Questions given in step # 13 6 × 0.5 point = 3 points
Question given in step # 14 2 points
Conclusion 2 points
Total Points: 20 Points
