Lecture 6Momentum, Relativity, Energy and Civilization

Chapter 3.8 3.15

Outline

• Linear Momentum• Angular Momentum• Relativity and Rest Energy• Energy and Civilization

Momentum

p = linear momentum m = mass v = velocity

Linear momentum

p = m v [p] = kg m/s

Linear momentum is a measure of tendency of an object to move at a constant speed along a straight line

Momentum is a vector

Conservation of momentum

In the absence of outside forces, the total momentum of a set of objects remains the same irrespective of interactions between them.

Total momentum = m1v1 = (m1+m2) v2

If the initial momentum was 0, then m1v1= m2v2

Demonstrations

Angular Momentum

Angular momentum is a rotational quantity that corresponds to linear momentum.

It describes the tendency of spinning objects to keep spinning.

Angular momentum is also a vector.Its direction coincides with the spin direction.

Relativity

The theory of relativity was proposed by Albert Einstein in 1905.

Relativity links space and time as well as matter and energy.

There are 2 parts of the theory: special relativity and general relativity.

Special relativity considers only constant velocities.General relativity includes acceleration.

Basis for Special Relativity

The laws of physics are the same in any inertial (that is, non-accelerated) frame of reference.The laws of physics observed by an observer traveling at some constant velocity must be the same as those observed by a stationary observer.

The speed of light is the same for all observers, no matter what their relative speeds.

c = 3 108 m/s = 300,000 km/s = 186,000 mi/s

Effects of Special Relativity

In a reference frame moving with a constant velocity v:Length of an object is L0

Its mass is m0

A time interval is t0

In a stationary reference frame the same quantities will be: L, m, t.

L < L0

m > m0

t > t0

The differences (ratios) depend on the ratio v/c: = 1/ (1 v2/c2) ≥ 1

Rest Energy

Mass and Energy are related to each other and can be converted into each other.

The rest energy of a body is the energy equivalent of its mass.

E0 = m0c2

E0 (m=1 kg) = 1 kg x (3 108)2 (cm/s)2 ~ 1017 JPE (m=1 kg, h=9 km) = mgh = 1 kg x 9.8 m/s2 x 9000 m ~ 105 J

General Relativity

Theory of general relativity was published in 1916.

It relates gravitation to the structure of space and time.

Gravity can be described as warping of spacetime around a body of matter a nearby mass tends to move toward the body.

Spacetime warping

Observational testing of general relativity

The Energy Problem

Until recently the energy consumption by the mankind was small with respect to the amount of available nature resources.

The natural resources include: water, coal, natural gas, oil, sources of nuclear energy.

Current problems:

Limited resources of fossil fuels (e.g., oil and natural gas).Air pollution due to fuel burning.Radioactivity of the nuclear fuel.

Possible Solutions of the Energy Problem

• Make energy consumption more efficient• Using alternative sources of energy (wind,

geothermal energy, solar energy, fusion nuclear reactions)

Both solutions require technology development science is very important!

Summary

• Conservation of energy and momenta work in any physical process

• The energy problem may become a serious issue for the mankind during the current century

• Theory of relativity expands the classical (Newtonian) mechanics to all possible velocities