Lecture 1: units, dimensions, measurements and associated uncertainties.
In this lecture Professor Walter Lewin introduced the three fundamental units in physics. They
are length, time, and mass; symbol L for length, T for time, and M for mass. All other quantities
can be derived from these fundamental quantities. For example, the dimension of speed is
[L]
[T]
.
Professor Lewin stressed that any measurements without knowledge of its uncertainties is
meaningless. To demonstrate his point, he brings up a story of his grandmother. His grandmother
once told him that a person lying down is longer than someone standing up. He first tested this
with an aluminum bar, first measured the length of the bar in vertical position, he got a length of
149.9 cm, with an uncertainty of ±0.1 cm. Then he measured the length of the bar in horizontal
position, this time the length was 150.0 cm, also with an uncertainty of 0.1 cm. Because the
difference of the two lengths is within the errors in the measurements, the bar is not longer in
horizontal position than in vertical position. Professor Lewin next repeated the experiment with a
student. This time, he found that the difference in the height was 2.5 cm ± 0.2 cm. This proves
that a person is longer when lying down than standing up. Professor Lewin therefore shows the
important of including uncertainties in the measurement.
Lecture 2: introduction to kinematics.
Average velocity can be computed by the difference in position divide by the different time
which it takes for the object to travel. If Xt1 denote X at time t1, and Xt2 denote X at time t2. Then
the average velocity of the object is given by the equation: 𝑉𝑡1 𝑡1 =
𝑋𝑡1 − 𝑋𝑡1
𝑡1 −𝑡2
. The velocity can
also be seen on a graph. Pick any two points, and find the slope of the line between the two
points. Find the angle that the line makes with the two points. If the angle is positive, then the
average velocity is positive, but if the angle is negative, then the average velocity is negative.
And 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑆𝑝𝑒𝑒𝑑 =
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑡𝑖𝑚𝑒
.
Lecture 3: Vector addition and subtraction.
A vector is something that has a length and a direction. There are two different ways of adding
two vectors. One is to bring the tail of one vector to the head of another, then draw a line from
the tail of the second vector to the head of the first. The result is the sum of the two vectors. The
other way is to put the tail of one vector to the tail of the next, then make a parallelogram using
the two vectors. The diagonal of the parallelogram is the sum of the two vectors. One can
immediately see that the order which you add the vectors make no difference, hence the
communitive law of vector addition. Vector subtraction is the same as adding a negative vector.
A negative vector is a vector that goes in the opposite direction. A vector is a point when looking
at it head on, and it is a cross if looking from behind.
Lecture 4: 3D Kinematics – free falling reference frames.
In this lecture, Professor Lewin applied what we had learned in lecture in the 3D ballistics
trajectory of a ball. If a ball is shot at a velocity 𝑉0, and at angle α from the x-axis, we would
know that the velocity in the x direction will never change, because there is no acceleration in the
X direction. So the velocity in the X direction can be given by 𝑉0𝑥 = 𝑉0 𝐶𝑜𝑠𝛼. However in the Y
direction, there is acceleration from gravity, and to find the velocity of the ball in the Y direction
at any point in time will need this equation 𝑉𝑦𝑡 = 𝑉0𝑦 + 𝐴𝑦 𝑡. If we were to find the highest point
which the object can reach, then we will need to solve for when the acceleration in the Y
direction is 0, which will give us 𝑡 =
𝑉0 𝑆𝑖𝑛𝛼
𝑔
, where g is acceleration of gravity.
Lecture 5: Uniform circular motion
If an object is traveling along a circular trial and its speed is constant, then it is called uniform
circular motion. The velocity is constantly changing, but the speed is not. Professor Lewin
introduced two new variables: T – the amount of time, in seconds, for the object to go around
once, and F – number of rotations per seconds, also known as hertz. We can immediately see that
1
F = T. Professor Lewin also introduced angular velocity, represented by the symbol Ω. It is
measured in radians per second. Thus Ω =
2𝜋
𝑇
. Then the velocity would be Ωr. There must be an
acceleration which changes the velocity constantly, and allows the object to turn in a circle. We
call it centripetal acceleration, and the symbol 𝑎𝑐 . Therefore the centripetal acceleration is given
by |𝑎𝑐 | =
𝑣2
𝑟
= Ω2 𝑟.