Cm 1a circular motion mathematical description (shared)
Cm 6 newton's law of gravitation (shared)
1. A-level Physics
Unit G484:
The Newtonian
World
Newton’s law of gravitation
Circular motion
2. Gravitation – lesson 1 recall LOs
To do/answer
1. Complete the following:
‘a field is a region of space in which a particular type of
object experiences a … ‘
2. Name the type of object needed to detect the following:
a. a magnetic field b. an electric field c. a gravitational field
3. Sketch a diagram to show the gravitational field in this lab.. Be ready to
explain what you are attempting to show.
4. Sketch a diagram to show the Earth’s gravitational field. How do we
describe this field? Where do the field lines i) come from, ii) go to?
What have you assumed about the Earth?
5. Define ‘gravitational field strength’.
Circular motion
3. Lesson focus
• Newton’s law of universal gravitation
Learning objectives
At the end of the lesson you will be able to:
• state Newton’s law of gravitation;
• select and use the equation for centripetal force F = -GMm/r2 for the
force between two point or spherical objects.
Circular motion
4. Learning outcomes
All of you should be able to
• state Newton’s law of gravitation in words;
• state this law as an equation and define the symbols used;
• use this equation to solve simple problems.
Most of you will be able to
• use Newton’s law of gravitation to solve more complex problems.
Circular motion
5. The gravitational force between objects LOs
Imagine two masses
m1 m2
We know that masses give rise to gravitational fields. Each mass will,
therefore, be in the gravitational field of the other.
1. Sketch the situation and show the forces on each mass.
2. List the factors that determine the size of the forces on the
masses.
Isaac Newton and gravity: video
Circular motion
6. Newton’s law of universal gravitation LOs
This law states that the
‘gravitational force between two point masses is proportional to the
product of the two masses and inversely proportional to the square of
the distance between them’.
G m1 m 2
F = -
r2
G - universal gravitational
Notes: constant (‘big G’)
• a point mass has no spatial extent
• the minus sign in the equation shows that the force is attractive
Circular motion
7. Newton’s law of universal gravitation LOs
G m1 m2 where,
F = - G - universal gravitational
r2
constant (‘big G’)
2/3 Newton conceived of this force extending (instantaneously)
throughout the entire Universe (hence universal). He did not
attempt to explain the origin of the force.
Circular motion
8. Newton’s law of universal gravitation LOs
To do
Using the data given
find a value for G.
Data: G m 1 m2
• your mass F = -
• the mass of the Earth (5.97 x 1024 kg)
r2
• radius of the Earth (6.37 x 103 km)
3/3 G is one of the least well defined constants of nature (hw: why is this?).
The accepted value is 6.674×10−11 N m2 kg−2 .
To do
Calculate the percentage difference between this and your value.
Circular motion