1. Ch. 7 (Section 7.3)
Circular Motion

2. Describing Circular Motion
An object undergoes acceleration moving at a constant speed. Explain!

3. Circular Motion Velocity
Recall v = Δd/Δt so in circular motion v= Δr/Δt
Velocity vector of object moving in a circle is tangent to the circle

4. Circular Motion Acceleration
Acceleration of object in uniform circular motion ALWAYS points towards middle of circle = centripetal acceleration

5. Centripetal Acceleration
Centripetal acceleration = (velocity)2 divided by the radius of the circle; ac = v2/r
ALWAYS points to center or circle!
To measure speed: measure the period, time (T) it takes for object to complete one revolution.
In one revolution distance = circumference of circle = 2πr so v = 2πr/T
If ac = v2/r then ac= (2πr/T)2÷r  4π2r/T2

6. Centripetal Acceleration Practice
A test car moves at a constant speed around a circular track. If the car is 48.2 m from the track’s center and has a centripetal acceleration of 8.05 m/s2, what is the car’s tangential speed?
a = v2/r

7. 2. A dog sits 1. 5 m from the center of a merry-go-round
2. A dog sits 1.5 m from the center of a merry-go-round. The merry-go-round is set in motion, and the dog’s tangential speed is 1.5 m/s. what is the dog’s centripetal acceleration?
a = v2/r

8. Centripetal Force Constant force applied causing circular motion
Recall 2nd Law: F = ma, if in uniform circular motion a = ac
So: Centripetal Force = Fc = mv2/r
Fc = m (4π2r/T2)
Points to center of circle, same direction as acceleration

9. Example Problem pg. 165
A 13-g rubber stopper is attached to a 0.93-m string and swung in a circle, making one revolution in 1.18 sec. Find the tension force exerted by the string on the stopper.

10. Nonexistent Force
Imagine you’re riding in a car and it suddenly stops, what happens to you?
Is there a force on you? Why/ why not?
Imagine riding in a car again, and it makes a sharp left turn, what happens to you?
Hence there is NOT an outward “force” on you, it is a fictitious force we call the centrifugal force, explained by Newton’s 1st Law

11. FUN DEMO

12. Changing Circular Motion: Torque
Point mass: object moving in circular path (ex. rubber stopper swung in circle, person on merry go round etc…)
Rigid rotating object: entire mass that rotates around its on axis (ex: a cd, the entire merry go round, a revolving door or ordinary door)

13. Torque How do you open a door? Should you push next to the hinges?
Should you push in, towards the hinges?
To open the door most easily, you push at a distance far from the hinges (axis of rotation), and in a direction perpendicular to the door.

14. Sesaw will balance when magda = mbgdb
Torque
Distance from the axis of rotation = lever arm
The product of the perpendicular force applied AND the lever arm = TORQUE
Greater torque = greater change in rotational motion
Sesaw will balance when magda = mbgdb

15. Chapter 8

16. Newton’s Law of Universal Gravitation
Everything pulls on everything else!
Greater the mass = greater the force
Greater the distance = weaker the force
Force = (mass1 x mass2)
(distance)2

17. The Universal Gravitation ConstantM m

18. What is the force of gravity between a 100 kg astronaut and a 50 kg astronaut floating 2 m apart in deep space?

19. How strong is the gravitational force between Mercury and the sun?
Mass (kg)
Distance from Sun (km)
Sun
1.99x1030
Mercury
3.30x1023
57,895,000

20. How strong is the gravitational force between Earth and the sun?
Mass (kg)
Distance from Sun (km)
Sun
1.99x1030
Earth
5.97x1024
149,600,000

21. Calculate the force of gravity on you, at Earth’s Surface
1 pound = ~4.45 Newtons
Mass of Earth = 5.97×1024 kg
Radius of Earth = 6.38×106 m

22. Section 8.2: Using the Law of Universal Gravitation

23. Gravity can be a Centripetal Force
Center seeking
Any force that is directed at right angels to the path of a moving object that tends to produce circular motion

24. Centripetal Force Keeps the Moon and Planets Where they Are!

25. Satellites and Gravity
The force of the Earth’s gravity keeps satellites in orbit
Satellites have horizontal velocities large enough that their falling distance is equal to the curvature of the Earth
29,000km/hr

26. What would happen to Earth if…
The sun’s gravity increased?
The Earth’s inertia decreased?
The Earth’s inertia increased?
Balance is key for and orbit to happen!

27. Combining Equations to solve for Orbital speed and Period
Recall Fc = mv2/r & F = GMEm/r2
GMEm/r2 = mv2/r
getting V by itself:
 v = √GME/r
Period: T = 2π√r3/GME
Both speed, v & period, T are independent of mass

28. Example Problem Pg. 187
A satellite orbits Earth 225 km above its surgace. What is its speed in orbit and its period?
Radius of Earth = 6.36 × 106 m
Mass of Earth = 5.97 × 1024 kg
G = 6.67 × N*m2/kg2

29. Gravitational Field gravity is always in the direction of the force
To find strength of the field you can place a small body of mass (m) in the field and measure the forceon the body
g= F/m
on Earth’s surface the gravitation field = 9.80 N/kg

30. Einstein’s Theory of Gravity
Einstein proposed that gravity is not a force but an affect of space itself
Mass causes space to be curved and other bodies are accelerated because of the way they follow this curved space