Section 5-2

Circular Motion; Gravitation

Reminder: AP test and solutions manual

giancoli physics principles with applications 6th edition solution manual3rd site in google gives a pdf Physics – Comcast.net

Objectives: The student will be able to:

• identify the type of force supplying the centripetal force that acts on any object in uniform circular motion.

• determine the directions of the velocity, acceleration, and net force vectors for an object in uniform circular motion.

• identify centrifugal force as a fictitious force and explain how it results from an accelerated frame of reference.

• use Newton's laws of motion and the concept of centripetal acceleration to solve word problems.

April 20, 2023

Uniform Circular Motion: Observations Object moving along a

curved path with constant speed Magnitude of velocity:

same Direction of velocity:

changing Velocity : changing Acceleration is NOT zero! Net force acting on an

object is NOT zero “Centripetal force”

amFnet

v

5-2 Dynamics of Uniform Circular Motion

For an object to be in uniform circular motion, there must be a net force acting on it.

We already know the acceleration, so can immediately write the force:

(5-1)

Uniform Circular MotionNewton’s 2nd Law: : The net force on a body is equal to the product of the mass of the body and the acceleration of the body.

*The centripetal acceleration is caused by a centripetal force that is directed towards the center of the circle.

F ma mv2

r

5-2 Dynamics of Uniform Circular Motion

We can see that the force must be inward by thinking about a ball on a string:

Demo – penny and hanger

5-2 Dynamics of Uniform Circular Motion

There is no centrifugal force pointing outward; what happens is that the natural tendency of the object to move in a straight line must be overcome.

If the centripetal force vanishes, the object flies off tangent to the circle.

““Centrifugal ForceCentrifugal Force””

• ““centrifugal forcecentrifugal force”” is a is a fictitious forcefictitious force - - it is not an interaction between 2 it is not an interaction between 2

objects, and therefore objects, and therefore not not a real forcea real force..

• NothingNothing pulls an object away from pulls an object away from the center of the circle.the center of the circle.

““Centrifugal ForceCentrifugal Force””

• What is erroneously attributed to What is erroneously attributed to ““centrifugal forcecentrifugal force”” is actually the action is actually the action of the objectof the object’’s s inertiainertia - whatever - whatever velocity it has (speed + direction) it velocity it has (speed + direction) it wants to keep.wants to keep.

April 20, 2023

Centripetal Force• Acceleration:

– Magnitude: – Direction: toward the center

of the circle of motion

• Force: – Start from Newton’s 2nd Law

– Magnitude:

– Direction: toward the center of the circle of motion

r

vac

2

r

vac

2

amFnet

vac

r

mvmaF cnet

2

netF

netF

netF

vFnet

netc Fa

||

April 20, 2023

What provides Centripetal Force ?

• Centripetal force is not a new kind of force• Centripetal force refers to any force that

keeps an object following a circular path

• Centripetal force is a combination of – Gravitational force mg: downward to the

ground– Normal force N: perpendicular to the surface– Tension force T: along the cord and away from

object– Static friction force: fs

max = µsN

r

mvmaF cc

2

April 20, 2023

a

What provides Centripetal Force ?

r

mvT

maTFnet

2

r

vmmgN

mamgNFnet

2

mg

N

v

Example ProblemA 2.0-kg mass is attached to the end of a 3.0 m-long rope and spun in a vertical circle at a speed of 6.6 m/s. Determine the maximum and minimum tensions in the rope.

April 20, 2023

Problem Solving Strategy• Draw a free body diagram, showing and

labeling all the forces acting on the object(s)• Choose a coordinate system that has one axis

perpendicular to the circular path and the other axis tangent to the circular path

• Find the net force toward the center of the circular path (this is the force that causes the centripetal acceleration, FC)

• Use Newton’s second law – The directions will be radial, normal, and tangential– The acceleration in the radial direction will be the

centripetal acceleration

• Solve for the unknown(s)

Circular Motion Lab

• Looking at factors affecting velocity. (graph for each part)• Part 1: Changing hanging mass and radius constant (100g, 200g, 250g, 300g, 350g,

400g) -Select at least 3 different masses with 3 trials. • Looking at centripetal force formula which indicates that centripetal force and velocity

squared are directly related. Prepare a graph to support this.• Data Table: Hanging weight; radius, mass of twirling object, number of revolutions,

elapsed time, period, velocity of twirling mass, centripetal acceleration.• 2nd Data Table: Hanging weight, Centripetal force of the twirling mass, % error• Part 2: Changing radius and keeping hanging mass constant (40 cm, 60 cm, 80 cm)

– At least 3 trials.• 2nd graph – see 1st bullet (think of the independent and dependent variables)

– Use a paper clip as a marker (always keep 1 cm below tube)– Swinging must be horizontal.– Must use SI units!– Goggles must be worn.– What causes the centripetal force?

Homework for Section 5-2

• Be prepared for lab.

• Problems 7, 8,13, 16, 18

Kahoot

• Section 5-2 Giancoli Dynamics of Uniform Acceleration