Uniform Circular Motion

Kinematics

Dynamics

Examples: curves on a road

Non-Uniform Circular Motion: Vector addition

Wait until chapter 8

Newton's Law of Gravity:

Orbits

Kepler's Laws

little g, big G

Forces and velocities

Review concepts

Position - velocity - acceleration

Changes in time

Changes in time

Scalar vs vector

If my velocity is constant can I have an acceleration?

If my speed is constant can I have an acceleration?

Uniform circular motion : the speed is uniform, and the acceleration is too. But only as we change our coordinate system

Kinematics of UCM

Using some trig relationships (similar triangles) and the definition of acceleration gives

An object moving in a circle of radius r at constant speed v has an acceleration pointing to the center with a value of:

Useful relationship

More Kinematics

Time to complete one revolution

Measured in seconds

(s)

Revolutions in one second

Measured in Hertz

(Hz)

Period:

Frequency:

Dynamics of UCM

Using Newton’s second law we see that there is a force required to move in a circular path.

This is not an additional force!!! Rather the net force. Meaning the sum of all forces in this radial direction.

It comes from other objects, and their associated forces.

Examples

Un-banked curves

Banked curves

Roller coaster

Tether ball

‘corners’

Aside: Centripetal vs. Centrifugal forces

Others?

F

F

F

fr

G

N

Radially and Tangentially

If a 1000 kg car goes around a 50 m radius turn, having tires with a static coefficient of friction of 0.6, how fast could it go before skidding out?

F

N

F

G

If it moves in a circle. a

If it goes faster or slower, than a

t

r

Non UCM

Newton's

Law of Universal Gravity.

It states that every particle in the universe

attracts every other particle.

and the force is proportional to the product

of the masses and inversely to the distance

between them squared

Further, that force is on a line between the

two particles

This is described in this equation:

Where G is a constant:

Acceleration due to gravity.

Yet we have said the force of gravity is

Force of

Gravity

mg

Weightlessness

When does someone 'feel' weightless?

Would both of these people 'feel' weightless?

You recall that if an object is to move

in a circular path, there must be a net

force acting on it pointing towards the

center.

This gravitational force is that force in

space physics.

Orbital Velocity

**Speeds in orbit**

**Think about the baseball.**

**slow down**

**Speed up**

**Closer =**

faster

faster

1. Path of each planet is ellipse with sun at one focus

2. Planets paths sweep equal areas in equal time

3. Ratio of period to radius between any 2 objects orbiting another is same

Kepler's Laws

For 3rd law, we will solve for this relationship in lab.

Which of these pairs can be compared using Kepler's 3rd Law?

A. Earth, and Moon

B. Earth and Satellite

C. Mars and Moon

D. Mars and Earth

E. Satellite and Mars

Try one

how long does it take Saturn to complete

one orbit?

Re = 149.6 x 10 km

Rs = 1427 x 10 km

6

6

What happens to a satellite in orbit

when its tangential or forward velocity increases:

A. It moves closer to earth.

B. Orbit stays the same.

C. It moves farther from earth.

Now that it is farther from earth what must it do to maintain that orbit distance?

A. Maintain this increased velocity

B. Return to previous velocity

C. Slow down to new velocity

D. Speed up to a new tangential velocity

"Also can you explain deterministic and weightlessness?"

"Should we go about the same set for for these problems like we did in chapter 4?"

"When talking about uniform circular motion, I couldn't help but wonder how a free body diagram is supposed to be drawn in order to show force in every circular direction. I'm guessing there's an equation that makes up for it?"

"Can we go over centrifuges?"

"How does the size not factor in to the force acting between them i mean in chemistry it does the bigger the more it pulls?"

7.36*10^22

5.98*10^24

1.90*10^27

1.99*10^30

2.80*10^30

3.50*10^30

DEMOS

Example: weight, when I lower an object