Circular Motion/Gravitation

 When an object is in uniform (speed is constant) circular motion, is it accelerating?

Yes

What is centripetal force? 

Net force on an object in circular motion

If an object is spun on a string in a horizontal circle overhead, which way will the object go if the string breaks?

In the direction of the velocity, which is tangent to the circle

Know how to calculate centripetal acceleration from velocity and radius.

v²/r

Know how to calculate centripetal force from velocity, radius, and mass.

mv²/r

What direction is centripetal acceleration?

Toward center of circle

Example of different forces that can cause centripetal force

Friction (car around a curve)

Example of different forces that can cause centripetal force

Tension (ball on a string)

Example of different forces that can cause centripetal force

Gravity (orbit)

Example of different forces that can cause centripetal force

Normal force (motorcycle on a circular path, or rollercoaster in a loop)

What causes Earth’s centripetal force, and which direction is this force pointed?

The sun; toward the center of the orbit, or toward the sun

What causes an object to go into orbit?

Tangential speed is so great that it “misses” the earth as the earth curves away from it

Are astronauts in orbit around the Earth weightless? Explain.

No, they are in constant free fall. Gravity keeps them in orbit!

How can the mass of the sun be measured?

Pick a planet. Measure it’s distance from sun and its speed.

How do the speeds of planets change as they get farther away from the sun?

The planets’ speeds decrease

If everything with mass exerts a gravity force on everything else with mass, why don’t we notice the gravity force between everyday objects?

Because their masses are too small to be noticeable

What provides the centripetal force for a car going around a curve?

Friction

If a car tried to go around a frictionless curve, what would happen?

It would keep going straight due to inertia and slide off the road

What provides the centripetal force for a ball spinning on a string?

Tension in the string

What provides the centripetal force to a passenger at the bottom of a loop in a roller coaster?

Normal force

 Be able to calculate orbital speed. Know that orbital speed does not depend on the mass of the orbiting object–only on the mass of the object being orbited.

Set mv²/r = to Newton’s Law. Or use the orbital velocity equation on the equation sheet which is the square root of GM/r. If you know the period and radius, use d = vT. (v = 2πr/T)

When solving dynamics problems with circular motion, the acceleration is…

v²/r , so F_net = ma = mv²/r

What is period, and what unit is used to measure it?

The amount of time it takes for one complete cycle (or revolution). It is measured in seconds

What is frequency, and what unit is used to measure it?

The number of cycles per second.  Hertz (Hz) which is 1/s.

 How is frequency related to period?

They are reciprocals

Kepler said that all orbits are what shape?

Ellipses

 Are planets at the center of their orbits?

No, they’re at one focus of the ellipse

What does Kepler’s second law say about the motion of planets?

They sweep out equal areas in equal times

Kepler’s third law describes a precise relationship between what two quantities?

Orbital radius and orbital period

What is angular velocity?

The number of radians per second that a rotating objects covers

If you know the period of a rotating object, how do find its angular velocity?

It is 2π divided by the period.

What is the symbol and unit for angular velocity?

Omega (ω). rad/s

What is the symbol and unit for angular acceleration?

Alpha (𝛼) rad/s²

 What is the angular counterpart to displacement, and what is its symbol and unit?

Angular displacement, which is measured in radians. Theta (𝜽) is the symbol