Uniform Circular Motion – Guided Notes Name___________________ Pd_____

Do Now… Remember the lab from last week?

A 13 g rubber stopper is attached to a .93 m string. The stopper is swung in a horizontal circle making one revolution in 1.18s. Find the tension force exerted by the string on the stopper.

a.) Identify your known and unknown information:

m = r = T = FT =

b.) Calculate the speed (v) of the stopper.

c.) Calculate the centripetal acceleration of the stopper (ac = v2/r).

d.) Use Newton’s Second Law to find the tension on the string.

UNIFORM CIRCULAR MOTION

Definition – When an object travels in a circular ___________ at a _____________ speed.

Speed is the _______________ of the velocity vector.

The direction of the velocity _________________ is changing

and therefore the __________________________________.

The acceleration of an object towards the center of it’s circular path of motion is called

_____________________ acceleration.

Uniform Circular Motion – Guided Notes Name___________________ Pd_____

VIDEO: REAL WORLD CENTRIPETAL FORCE

A planet orbits a star and a Ferris wheel curves around a central point because of _____________ __________.

The word ___________________ means center-seeking.

Centripetal Force:

FC=ma=

Satellites would continue to move in a straight line because of _______________,

________________ occurs because gravity is continuously changing the satellites direction.

CENTRIPETAL FORCE

When an object moves in a circular path, the net force towards the ___________of the circle is called centripetal force.

In the lab, the ______________ force of the string kept the stopper travelling in a circular path.

When a car is going around a bend, _____________ force between the tires and the road causes centripetal acceleration.

CENTRIPETAL FORCE – cont’d

_____________ _____________ keeps the International Space Station in orbit around the Earth.

Newton’s Law of ________________ Gravitation tells us that ____ objects are gravitationally attracted to each other.

We can calculate the strength of the gravitational force between any two objects using this formula.

Uniform Circular Motion – Guided Notes Name___________________ Pd_____

Fg=G

Example Problem – The International Space Station (ISS) orbits the Earth at an average height of 3.7 x 105 m above the Earth’s surface. The Earth has a radius of approx. 6.4 x 106 m and a mass of 5.97 x 1024 kg. Given that the mass of the ISS is 450,000 kg…

a.) Calculate the gravitational attraction between the ISS and the Earth.

b.) Find the speed at which the ISS orbits the Earth (orbital speed).

Uniform Circular Motion – Guided Notes Name___________________ Pd_____

Homework Problem #1 – Given that the Sun (MS = 1.99 x 1030 kg) and the Earth (ME = 5.97 x 1024 kg) are separated by a distance of 1.5 x 1011 m.

a.) Calculate the gravitational attraction between the Earth and the Sun.

b.) Calculate the orbital speed of the Earth around the Sun.

c.) Challenge! Calculate the orbital period of the Earth around the sun. What is the term we use to define the amount of time it takes for the Earth to make one revolution around the sun?

Bonus Problem - A satellite (such as the ISS) that is always the same height above the Earth moves in uniform circular motion. Derive a general formula for orbital speed of a satellite around Earth. *Hint: Gravitational force causes the centripetal acceleration of the satellite towards the center of earth. So we can say

Fnet=Fg=Gm1m2

r2

Fnet=mac=mv2

r

Uniform Circular Motion – Guided Notes Name___________________ Pd_____