Uniform Circular MotionUniform Circular MotionWhat is the object being forced to do as a unbalanced force is Being applied?

What was the equation for velocity?

What would be the equationFor an object revolving in a circle?

Revolution?

Period?

What do these numbers What do these numbers represent?represent?

Mercury . . . 88 earth days

Venus . . . 225 days

Earth . . . 365 days

Mars . . . 685 days

Jupiter . . . 12 earth years

Saturn . . . 29 years

Uranus . . . 84 years

Neptune . . . 165 years

Pluto . . .

Calculating T and VelocityCalculating T and VelocityWhat is a period, and what does it stand for?

What is the period, if takes a merry go round 30 seconds to make 5 revolutions?

A ball with a mass of 3.0kg is whirled by a student.The distance from the ball to the center of rotation is 4.0m. The time for one revolution is 2.0sec. What is the velocity of the ball.

Zena the African warrior revolves a rope with rocks on the end of it with a radius of 1.5meters. She gets 15 revolutions in 10 seconds before she lets it go to kill a wambat. How fast was her weapon moving before she let it go?

A

B

C

Circular MotionCircular Motion

A ball is going around in a circle attached to a string. If the string breaks at the instant shown, which path will the ball follow?

16

B: Ta

ngen

t to

the

B: Ta

ngen

t to

the

Circl

e

Circl

eInertia?

http://www.youtube.com/watch?v=RWeJWchXosY://

Types of Weapons that use Types of Weapons that use Tangential VelocityTangential Velocity

Uniform Circular motionIs it Accelerating?

v

mg

FN

FTr

m

mw

FN = mg

FT = Tension Force

F= maFc = m (v2 / r)

Uniform Circular motion

Uniform circular motion in a horizontal plane

v

mg

FN

FTzr

m

M

Fc= m (v2 / r)

• Tension suddenly disappears and there is no more centripetal

force• Circular motion cannot be maintained.• The rubber stopper will move with its velocity tangent to the

circle at the instant the string breaks

v

mg

FN

FTzr

m

M

v

mg

FN

FTzr

m

M

v

mg

FN

FTzr

m

M

Name 3 events as a result of a cable suddenly breaking:

Multipliers1.How does changing a variable affect the centripetal acceleration? Manipulate the formula directly.If aC = 15 m/s2, what if:

i. The mass is doubled:

ii. The mass is halved:

ii. The velocity is doubled:

iiii. The velocity is tripled:

v. The velocity is halved:

vi. The velocity is quartered

vii. The radius is quadrupled

viii.The radius is halved:

MultipliersHow does changing a variable affect the centripetal acceleration? Manipulate the formula directly.If FC = 15 m/s2, what if:

i. The mass is doubled:

ii. The velocity is doubled:

iii. The velocity is halved:

iv. The radius is halved:

Fc = m (v2 / r)

What is the physical meaning of the formula?

Ac=V2/r

A Ball with a mass of 3.0kg is whirled overhead by a student. The distance from the ball to the center of rotation is 4.0m.The time for one revolution is 3.0 sec.

i.Find the velocity of the ball

ii.Find the centripetal acceleration

iii.Find the centripetal force

iv.Sketch the system, showing the magnitude and direction of the ball whirling overhead. Be sure to label all forces acting on the ball

V=2∏R/T

T=Tt/#of revolutions

Circular Motion ReviewCircular Motion Review

When we see an object When we see an object carrying out circular motion, carrying out circular motion, we know that there must be we know that there must be force acting on the object, force acting on the object, directed towards the center directed towards the center of the circle.of the circle.

When you look at the circular When you look at the circular motion of a ball attached to motion of a ball attached to a string, the force is provided a string, the force is provided by the tension in the string.by the tension in the string.

When the force responsible When the force responsible for the circular motion for the circular motion disappears, e.g. by cutting disappears, e.g. by cutting the string, the motion will the string, the motion will become linear.become linear.

Sample ProblemSample Problem

A 95 kg running back makes a turn on the football fieldThe halfback sweeps out a path that is a portion of a circle with a radius of a 12 meters, the halfback makes a quarter turn around the circle in 2.1 seconds. Determine the speed, acceleration, and the centripetal force?

Circular Motion with FrictionCircular Motion with Frictionbeing the Centripetal Forcebeing the Centripetal Force

Circular Motion and its Circular Motion and its Connection to FrictionConnection to Friction

When you drive your car around a When you drive your car around a corner you carry out circular motion.corner you carry out circular motion.

In order to be able to carry out this In order to be able to carry out this type of motion, there must be a type of motion, there must be a force present that provides the force present that provides the required acceleration towards the required acceleration towards the center of the circle.center of the circle.

This required force is provided by the This required force is provided by the friction force between the tires and friction force between the tires and the road.the road.

But remember ….. The friction force But remember ….. The friction force has a maximum value, and there is a has a maximum value, and there is a maximum speed with which you can maximum speed with which you can make the turn.make the turn.

Required force = Mv2/r.If v increases, the friction force must increase and/or the radius must increase.

Lets Think About it?Lets Think About it?Rex Things and Doris Locked are out on a date. Rex makes a rapid right-hand turn. Doris begins sliding across the vinyl seat (that Rex had waxed and polished beforehand) and collides with Rex. To break the awkwardness of the situation, Rex and Doris begin discussing the physics of the motion that was just experienced. Rex suggests that objects which move in a circle experience an outward force. Thus, as the turn was made, Doris experienced an outward force that pushed her towards Rex. Doris disagrees, arguing that objects that move in a circle experience an inward force. In this case, according to Doris, Rex traveled in a circle due to the force of his door pushing him inward. Doris did not travel in a circle since there was no force pushing her inward; she merely continued in a straight line until she collided with Rex. Who is correct? Argue one of these two positions.

When the turn is made, Doris continues in a straight-line path; this is Newton's first law of motion. Once Doris collides with Rex, there is then an unbalanced force capable of accelerating Doris towards the center center of the circle, causing the circular motion.

Circular Motion Circular Motion Problem?Problem?

A 2000. kg car rounds a circular turn of radius 25 m. If the road is flat and coefficient of static friction between the tires and road is 0.70, how fast can the car go without skidding?A 2000. kg car rounds a circular turn of radius 25 m. If the road is flat and coefficient of static friction between the tires and road is 0.70, how fast can the car go without skidding?

A 2000kg Car rounds a circular turn of radius of 25m. If the road is flat and coefficient of static friction between the tires and the road is .70. How fast can the car go without skidding

Work

Questions 2Questions 2You are driving a car with constant speed around a horizontal circular track. On a piece of paper, draw a Free Body Diagram for the car. You are driving a car with constant speed around a horizontal circular track. On a piece of paper, draw a Free Body Diagram for the car.

How many forces are acting on the car?How many forces are acting on the car? A) 1 A) 1 B) 2 B) 2 C) 3 C) 3 D) 4 D) 4 E) 5E) 5

25

The net force on the car isThe net force on the car is A. Zero A. Zero B. Pointing radially inward B. Pointing radially inward C. Pointing radially outwardC. Pointing radially outward

Gravity

Tension

3 forces, Tension (friction), gravity and the normal force

B: Force of tension is pointing inward

Normal

Question 3Question 3Davain sits on the outer rim Davain sits on the outer rim of a merry-go-round, and of a merry-go-round, and Diego sits midway between Diego sits midway between the center and the rim. The the center and the rim. The merry-go-round makes one merry-go-round makes one complete revolution every complete revolution every two seconds.two seconds.– Diego’s velocity is:Diego’s velocity is:

(a)(a) the same as Davian’s

(b)(b) Faster than Davian’s

(c) Slower than Davian’s

Diego Davian

a = V2/r(C) Diego is slower than the velocity of Davian

SummarySummary

Uniform Circular MotionUniform Circular Motion– Speed is constantSpeed is constant– Direction is changingDirection is changing– Acceleration toward center a = vAcceleration toward center a = v22 / r / r– Newton’s Second Law F = maNewton’s Second Law F = ma

Universal law of GravitationUniversal law of Gravitation

Explain Newton’s Law of Universal Explain Newton’s Law of Universal Gravitation.Gravitation.

Formula?

Gravitational Pull PhenomenaGravitational Pull Phenomena

Explain the inverse-square law that Explain the inverse-square law that Newton determined directly Newton determined directly determined the force of gravity.determined the force of gravity.

RelationshipsRelationships

Multipliers Again? What up!Multipliers Again? What up!

How does changing a variable affect How does changing a variable affect the gravitational force? the gravitational force? Manipulate the formula directly.Manipulate the formula directly.

  If FIf FGG = 15 N, what if: = 15 N, what if:

1.the mass of m1 is doubled:2.both masses are halved:3.m1 is doubled and m2 is halved:4.the distance is tripled:5.the distance is halved:6.the distance is quartered7.the distance is quadrupled8.the distance is doubled:

Problem?Problem?

Two 10.0 kg bowling balls are 50 m Two 10.0 kg bowling balls are 50 m apart. What is the gravitational force apart. What is the gravitational force between these two objects? What is between these two objects? What is the gravitational potential energy?the gravitational potential energy?

Two More ProblemsTwo More Problems

The mass of the Earth is 5.98 x 10The mass of the Earth is 5.98 x 102424 kg and its radius is 6.37 x 10kg and its radius is 6.37 x 1066 m. m. Determine the acceleration of gravity Determine the acceleration of gravity on the surface of Earth. This answer on the surface of Earth. This answer has to be in newtons.has to be in newtons.

Calculate the Magnitude of the gravitational force of attraction that Earth exerts on the moon.