AP Physics
Do the following practice exercises this weekend. (The answers are provided on another document so that you
can get feedback.) Hopefully, most if not all of this will be review. If something seems new to you or if your
experience with it is limited, then you should research how to do it on the internet so that you are at least
familiar with it before class on Monday. Topics in vector mathematics will be introduced as needed early in the
course.
DAY 1
Algebra Review: solve the following equations for the variable indicated.
1. C = 2πr for r
2. V = 4𝜋𝑟2 for r
3. v = vo + at for t
1
4. x = xo + vot + at2 for t
2
𝑙
5. T = 2π√ for g
𝑔
1
6. mgh = mv2 for v
2
7. v2 = vo2 + 2a(x – xo) for a
8.
1
𝑓
=
1
𝑠0
+
1
𝑠𝑖
for si
Calculations Review: do the following calculations rounding the answer to the proper number
of significant digits and simplify the units.
2
9. I = (7.2 𝑥 103 𝑘𝑔)(8.32 𝑥 108 𝑚)2
5
(8.99 𝑥 109 𝑁𝑚2 /𝐶 2 )(−2.8 𝑥 10−5 𝐶)(3.4 𝑥 10−5 𝐶)
10. F =
11.
1
𝑹
=
1
2.5 𝑥 104 𝛺
+
1.5 𝑥 10−2 𝑚2
1
5.0 𝑥 104 𝛺
find R
12. 1.45 sin 36o = sin Θ, find Θ
13. T = 2π√
1.24 𝑥 10−3 𝑚
𝑚
9.8 2
𝑠
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DAY 2
Unit Conversions – Dimensional Analysis Review:
The study of physics, like most other sciences, uses the MKS (meter, kilogram, and second) or
SI system of units to describe physical quantities in nature. Convert the following quantities to
the desired units. You might have to look up the equality between units.
14. 29.5 cm = ______ m
15. 945.87 g = ______kg
16. 593.17 ms = ______ s
17. 10.63 km = ______ m
18. 8.485 cg = ______ kg
19. 1.96 x 10 -4 s = ______ s
20. 3.00 x 105 m/s = _______m/s
21. 0.032 km2 = _______ m2
22. 386.73 cm/minute = ________ m/s
Geometry Review
23. Find the unknown angles for Θ, below.
a.
Θ
b.
90o
Θ
25o
2
24.Find the unknown sides
a. X = ______
60o
7m
X
45o
b. Y = ______
5 m/s
Y m/s
DAY 3
Trigonometry Review
Use the generic triangle right triangle below, basic trigonometry, and the Pythagorean
Theorem to solve the following. NOTE: Your calculator must be in the degree mode.
c
b
Θ
a
25.
a)  = 55o and c = 32 m, solve for a and b. _______________
b)  = 45o and a = 15 m/s, solve for b and c. _______________
c) b = 17.8 m and  = 65o, solve for a and c. _______________
d) a = 250 m and b = 180 m, solve for  and c. _______________
e) a =25 cm and c = 32 cm, solve for b and . _______________
3
Vectors and Vector Quantities - Review (or possibly new)
Vectors
A lot of physical quantities in nature are best described by a vector. Therefore it is very important that one
becomes confident and proficiency in using vectors.
Just like in the movie Despicable Me all vectors have both magnitude (also known as size) and direction. The
magnitude of a vector is just a numerical value with the associated units. The direction indicates the
orientation of the quantity with respect to some other specified position. A few examples of vector quantities
are velocity and force.
Most students are very familiar with scalar quantities. These are physical quantities that are described solely
by a numerical value with units. Mass in kilograms and time in seconds are examples of scalar quantities.
Scalars have magnitude only. Scalar mathematics is pretty much what you have done in your mathematics
classes up till now.
Vectors have their own types of notation: Examples include A, or A.
Vectors have a geometric quality to them. Therefore, they can be graphically represented by an arrow, where
the length of the arrow is proportional to the vectors magnitude. And the direction the arrow points is the
direction of the vector.
Negative Vectors
Negative vectors have the same magnitude as their positive counterpart. They are just pointing in the opposite
direction.
A
-A
B
-B
Vector Addition and subtraction
Think of vector addition or subtraction as vector addition only. A – B = A + (-B)
The result of adding vectors is called the resultant, R. NOTE: the A and B are added together in the head-to-tail
method below.
A+B=R
A
+
B
=
R
B
A
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Any two vectors that are collinear (acting along the same line or direction) can be added (or subtracted) just
like scalar quantities. For example (see below), if A has a magnitude of 3 and B has a magnitude of 2, then R
has a magnitude of 3+2=5.
A
B
+
A
=
B
R
Note: this is still the head-to-tail method, but since the vectors are collinear it’s very easy to determine the
direction of the resultant – unlike the previous example.
When subtracting a vector from another, think of the one subtracted as being a negative vector (the same
magnitude but pointing the opposite direction).
So A – B = A + (-B)…= 5 + (-2) = +3
B
A
A
-B
R
IMPORTANT NOTE: In physics a negative number does not always mean a smaller number. Specifically when
encountering vector quantities. Mathematically –2 is less than +2 on a number line, but if these are vectors
(say -2 meters and + 2 meters of displacement), they have the same magnitude (size), they just point in
different directions (180o apart).
Practice with vectors in 1-D (collinear vectors)
26. Add the following vectors.
a. 5 m East
b. 2 m West
c.
added to 7 m East
added to 11 m West
3 m North
added to 8 m North
d. 6 m South
added to 9 m South
27. Subtracting collinear vectors. For a – d above subtract the second vector from the first.
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DAY 4
Finding the components of vectors
Since by definition every vector contains two pieces of information – a magnitude (or size) and a direction, one
can decompose/analyze any vector as a sum of two vectors. Another way to look at this is that any vector can
be considered a resultant of two vectors added together – a horizontal vector (horizontal component) and a
vertical vector (vertical component). The advantage to decomposing vectors is that it makes the addition or
subtraction of any number of vectors a much simpler process. This is because the addition (or subtraction) of
the horizontal and vertical components is just like that accomplished in questions 26 and 27 above. The
resultant of any number of vectors can then be obtained by adding the sum of all the horizontal components
together with the sum of all the vertical components together.
How does one go about finding the horizontal and vertical components of a vector? Answer: by using the sine
and cosine functions. The whole process of adding two vectors is illustrated in the following example.
EXAMPLE: Suppose a hiker travels in a straight line 2.8 kilometers at an angle of 30 o North of West. At this
new location she then travels 5.0 kilometers at an angle of 60 o North of South. How far and in what direction
must someone travel from the hiker’s starting point to meet the hiker (assuming the hiker doesn’t move after
the second leg of her trip). The diagram below shows an approximation of her trip.
R
? km + direction?
N
R
5.0 km
5.0 km
B
N
B
A
A
2.8 km
2.8 km
E
Ay=+ (2.8km) sin 30o
W
Ax=+ (2.8km) cos 30o
E
W
S
S
Note that each of the given vectors can be considered the hypotenuse of a triangle with horizontal and vertical
components that make up the other legs/sides of the triangle. Therefore given the hypotenuse length and its
angle from the horizontal (or vertical) axis, one can use the sine and cosine functions to find the lengths of the
horizontal and vertical components of the given vector. See how the components of A have been found in the
second diagram above.
28. Find the components for B. Notice the horizontal component of B must be negative because it points to the left.
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29. Find the sum of the horizontal components of A and B. This is the horizontal component of R.
30. Find the sum of the vertical components of A and B. This is the vertical component of R.
31. Sketch a picture of these two components added together head-to-tail and adding R as the hypotenuse.
32. Now calculate the length of R using the Pythagorean theorem.
33. Finally calculate the angle of R using the tangent and the lengths of the components of R -
Congratulations! You have just learned how to find the sum of any two vectors. Now do another vector addition for
practice entirely by yourself.
34. Add the following vectors: 4 km at 45o north of east, and 8 km at 30o south of east. Start by sketching the two added
together head-to-tail.
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