Download Dynamics of Circular Motion

Dynamics of Circular Motion
by SHS Encoder 3 on June 17, 2017
lesson duration of 42 minutes
under General Physics 1
generated on June 17, 2017 at 09:48 am
Tags: Dynamics of Circular Motion
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Generated: Jun 17,2017 05:48 PM
Dynamics of Circular Motion
( 1 hour and 42 mins )
Written By: SHS Encoder 3 on July 2, 2016
Subjects: General Physics 1
Tags: Dynamics of Circular Motion
Resources
University Physics with modern Physics (12th ed.)
Young, H. D., & Freedman, R. A. (2007). University Physics with modern Physics (12th ed.). Boston, MA: AddisonWesley.
Physics for scientists and engineers: A strategic approach with modern Physics and mastering Physics
Knight, R. (2007). Physics for scientists and engineers: A strategic approach with modern Physics and mastering
Physics.
Physics. New York: Pearson Education.
Conceptual Physics
Hewitt, P. G. (2006). Conceptual Physics.
Physics. San Francisco: Pearson Addison Wesley
Content Standard
The learners demonstrate an understanding of...
1. Newton’s Law’s of Motion
2. Inertial Reference Frames
3. Action at a distance forces
4. Mass and Weight
5. Types of contact forces: tension, normal force, kinetic and static friction, fluid resistance
6. Action-Reaction Pairs
7. Free-Body Diagrams
8. Applications of Newton’s Laws to single-body and multibody dynamics
9. Fluid resistance
10. Experiment on forces
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11. Problem solving using Newton’s Laws
Performance Standard
The learners are able to solve, using experimental and theoretical approaches, multiconcept, rich-context problems
involving measurement, vectors, motions in 1D, 2D, and 3D, Newton’s Laws, work, energy, center of mass,
momentum, impulse, and collisions
Learning Competencies
The learners apply Newton’s 2nd law and kinematics to obtain quantitative and qualitative conclusions about the
velocity and acceleration of one or more bodies, and the contact and noncontact forces acting on one or more bodies
INTRODUCTION AND MOTIVATION 10 mins
1. Whirl the ball attached to a string in a horizontal circle above your head. You may also ask for a learner volunteer to
do this.
2. Ask the learners to describe the motion of the object.
ANSWER: The ball is in circular motion.
3. Ask the learners to identify the forces acting on the ball. Also ask the direction of the forces.
ANSWER: Tension directed toward your hand or the center of the circular path; gravitational force (weight of the ball)
directed downward; drag force directed upward.
4. If you whirl a ball attached to string around your head, it moves in a circular path around you because the string is
always pulling the ball directly toward the hand grabbing the string. The ball wants to move in a straight line and the
string is pulling it directly inward. The resulting deflection is a compromise: a circular path.
5. Ask the learners what will happen if you let go of the string.
ANSWER: The string is applying a centripetal force to the ball: an inward force. If you let go of the string, there is no
centripetal force and the ball will fly off in a straight line because of its inertia.
INSTRUCTION/DELIVERY 25 mins
1. Recall uniform circular motion.
Recall that for uniform circular motion the radial acceleration is given by:
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2. Discuss centripetal force.
From Newton’s Second Law, we know that if an object is accelerating there is a net force that is causing the
acceleration. For the case of uniform circular motion, this force is called the centripetal force. The net inward radial
force on the particle is given by
. Fnet can be from any combination of forces that induces the
circular motion. For the case of the demonstration, the force that induced circular motion Note that the net force and
acceleration are directed toward the center of the circular path as shown in Figure 1.
Figure 1. In uniform circular motion, the net force and acceleration are directed toward the center of the circular path.
3. Discuss what will happen if the centripetal force became zero.
If the object was initially moving in a circular path and then the centripetal force was suddenly removed, according to
Newton’s First Law, the object will move in a straight line with constant speed. This constant speed is equal to the
tangential speed of the object. For the case of the ball in our demonstration earlier, the string is applying a centripetal
force to the ball: an inward force. If you let go of the string, there is no centripetal force and the ball will fly off in a
straight line as shown in Figure 2.
Figure 2: If the centripetal force became zero, the object will move in a straight line with constant speed according to
Newton’s First Law of Motion
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4. Discuss how to draw the free-body diagram of objects in uniform circular motion.
Again note that Fnet can be from any combination of forces that induces the circular motion. In a free-body diagram,
this force that causes the object to move in a circular path should be drawn as a vector pointing towards the center of
the circle. Note that the quantity
is not a force and therefore should not be included in the free-body diagram.
For example, a car moving in a horizontal circle on a level surface experiences 3 forces.
Figure 3: Drawing the free-body diagram of a car moving in a horizontal circle on a level surface
Applying the concept of a centripetal force requirement, we know that the net force acting upon the car is directed
inwards. Since the car is positioned on the left side of the circle, the net force is directed rightward. An analysis of the
situation would reveal that there are three forces acting upon the object—the force of gravity (acting downwards), the
normal force of the pavement (acting upwards), and the force of friction (acting inwards or rightwards). It is the friction
force which supplies the centripetal force requirement for the car to move in a horizontal circle. Without friction, the car
would turn its wheels but would not move in a circle (as is the case on an icy surface).
5. Demonstrate how to solve problems on the dynamics of circular motion. Choose two to three examples from the
worked problems on the dynamics of circular motion and discuss how to apply Newton’s Second Law of Motion to
solve each problem.
A. Model: Make simplifying assumptions.
B. Visualize: Draw a pictorial representation. Use rtzcoordinates.
rtzcoordinates. (r
(r – radial axis, directed towards the center of the
circle; t – tangential axis; z – z-axis, perpendicular to the plane of motion)
Establish a coordinate system with the r-axis pointing toward the center of the circle.
Show important points in the motion on a sketch. Define symbols and identify what the problem is trying to
find.
Identify the forces and show them on a free-body diagram.
C. Solve: Newton’s Second Law is
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Determine the force components from the free-body diagram. Be careful with signs.
The tangential acceleration for uniform circular motion is at = 0
Solve for the acceleration, then use kinematics to find velocities and positions.
D. Assess: Check that your result has the correct units, is reasonable, and answersthe question.
PRACTICE 13 mins
1. Let learners solve circular motion problems. Choose from the attached problems.
PRACTICE 13 mins
1. Let learners solve circular motion problems. Choose from the attached problems.
PRACTICE 13 mins
1. Let learners solve circular motion problems. Choose from the attached problems.
ENRICHMENT 2 mins
1. Give problem-solving assignments. Choose from the challenge problems.
ENRICHMENT 2 mins
1. Give problem-solving assignments. Choose from the challenge problems.
ENRICHMENT 2 mins
1. Give problem-solving assignments. Choose from the challenge problems.
ENRICHMENT 2 mins
1. Give problem-solving assignments. Choose from the challenge problems.
EVALUATION 10 mins
Ask the learners one to two conceptual questions on the dynamics of circular motion. Let them work in pairs so that
they can discuss possible answers.
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1. An out-of-gas car is rolling over the top of a hill at speed . At this instant,
a.
b.
c.
d. We can’t tell about
without knowing
.
2. In the figure is a bird’s-eye view of particles moving in horizontal circles on a tabletop. All are moving at the same
speed. Rank in order, from largest to smallest, the tensions Ta to Td. Give your answer in the form a > b = c > d and
explain your ranking.
3. Tarzan swings through the jungle on a vine. At the lowest point of his swing, is the tension in the vine greater than,
less than, or equal to the gravitational force on Tarzan? Explain.
EVALUATION 10 mins
Ask the learners one to two conceptual questions on the dynamics of circular motion. Let them work in pairs so that
they can discuss possible answers.
1. An out-of-gas car is rolling over the top of a hill at speed . At this instant,
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a.
b.
c.
d. We can’t tell about
without knowing
.
2. In the figure is a bird’s-eye view of particles moving in horizontal circles on a tabletop. All are moving at the same
speed. Rank in order, from largest to smallest, the tensions Ta to Td. Give your answer in the form a > b = c > d and
explain your ranking.
3. Tarzan swings through the jungle on a vine. At the lowest point of his swing, is the tension in the vine greater than,
less than, or equal to the gravitational force on Tarzan? Explain.
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