Please tear off this top page carefully (only the top page!!!).
The formula sheet is on the back of this page.
(You do NOT need to turn this page in with your exam.)
Use the example below to fill in your scantron form.
You must fill in the following information:
1.
Name:
“Last name” then “First name” with a space in between (don’t forget to fill in the bubble for a
space).
2.
UID:
8 digits where the first “u” has been replaced by a zero.
3.
Special Code:
“01” for version A and “02” for version B.
4.
Your answers:
There are 25 questions, so please use numbers 125 on the scantron form.
You do NOT need to fill in gender, date of birth, etc.
Angular Momentum
_
ܮ
ሬ⃗
௧௧
= ܫ߱
ሬ⃗
߬⃗
௫௧
=
݀ܮ
ሬ⃗
݀ݐ
ܮ
ሬ⃗
= ݎ⃗ × ⃗
Ω
=
ఛ
ೣ
(precession)
Ω
=
ௌ
ூ
ೞೖ
ఠ
(precessing disk)
Statics
_
∑ܨ = 0,
∑߬ = 0
(any axis)
ܽ
= 0,
ߙ = 0
Simple Harmonic Motion
_
ݔ(ݐ) = ܣ cos(߱ݐ + ߶)
ݒ(ݐ) = −ܣ߱ sin(߱ݐ + ߶)
ܽ(ݐ) = −ܣ߱
ଶ
cos(߱ݐ + ߶)
߱ = ට
ೖ
(mass on a spring)
߱ = ට
(simple pendulum)
߱ = ට
ೃ
(physical pendulum)
߱ =
ඥ
ഉ
(torsion pendulum)
߬ = −ߢΔߠ
(torsional torque)
Harmonic Transverse Waves
_
ௗ
మ
௬
ௗ௫
మ
=
ଵ
௩
మ
ௗ
మ
௬
ௗ௧
మ
(wave equation)
ݕ(ݔ, ݐ) = ܣ cos(݇ݔ − ߱ݐ)
ݒ
௪௩
= ߣ݂ =
ఠ
=
ఒ
்
(travelling wave)
݇ =
2ߨ
ߣ
߱ = 2ߨ݂
݂ =
1
ܶ
ݒ
௪௩
= ට
ഋ
(
wave on a string)
ܭ
௫
∝ ߱
ଶ
ܣ
ଶ
Standing Waves
_
ݕ(ݔ, ݐ) = 2ܣ(cos ݇ݔ)(cos ߱ݐ)
Systems of Particles
_
ܴ
ሬ⃗
=
∑ ݉
ݎ⃗
∑ ݉
ܸ
ሬ⃗
=
∑ ݉
ݒ
⃗
∑ ݉
ܣ
⃗
=
∑ ݉
ܽ
⃗
∑ ݉
ܨ
⃗
௫௧
= ܯ
௧௧
ܣ
⃗
ܭ
௦௬௦௧,
= ܭ
௧௩ ௧
+ ܭ
Translational Momentum
_
⃗ = ݉ݒ
⃗
ܨ
⃗
=
݀⃗
݀ݐ
ܲ
ሬ⃗
௧௧
= ܯ
௧௧
ܸ
ሬ⃗
∫ ܨ
⃗
௧
݀ݐ = ܨ
⃗
௩
∆ݐ = ∆⃗
(impulse)
Elastic Collisions
_
ܭ = ∑
భ
మ
݉
ݒ
ଶ
is conserved
หݒ
⃗
ଶ
− ݒ
⃗
ଵ
ห = ݒ
⃗
ଶ
− ݒ
⃗
ଵ

(approach speed = separation speed)
ݒ
ଵ
∗
 = หݒ
ଵ
∗
ห,
ݒ
ଶ
∗
 = หݒ
ଶ
∗
ห
(center of mass frame)
Rotational Kinematics
_
ݔ = ߠݎ
ݒ = ߱ݎ
ܽ = ߙݎ
߱ = ߱
+ ߙݐ
ߠ = ߠ
+ ߱
ݐ +
1
2
ߙݐ
ଶ
ൢ
ഀసೞೌ
Rotational Dynamics
_
߬⃗ = ݎ⃗ × ܨ
⃗
߬⃗
௧
= ܫߙ
⃗
ܫ = ∑ ݉
ݎ
ଶ
(discrete distribution)
ܫ = ∫ ݎ
ଶ
݀݉
(continuous distribution)
ܫ
௧௧
= ܫ
+ ܯܦ
ଶ
(parallel axis theorem)
ܫ
ௗ௦
=
1
2
ܯܴ
ଶ
ܫ
= ܯܴ
ଶ
ܫ
௦ௗ ௦
=
2
5
ܯܴ
ଶ
ܫ
ௗ,
=
1
12
ܯܮ
ଶ
ܫ
௦ ௦
=
2
3
ܯܴ
ଶ
ܫ
ௗ,ௗ
=
1
3
ܯܮ
ଶ
ܭ
௧
=
1
2
ܫ߱
ଶ
=
ܮ
ଶ
2ܫ
ܭ
௧௦
=
1
2
ܯܸ
ଶ
Kinematics
_
ݒ
⃗ =
݀ݎ⃗
݀ݐ
ܽ
⃗ =
݀ݒ
⃗
݀ݐ
ݒ
⃗ = ݒ
⃗
+ ܽ
⃗ݐ
ݎ⃗ = ݎ⃗
+ ݒ
⃗
ݐ +
1
2
ܽ
⃗ݐ
ଶ
ݒ
௫
ଶ
= ݒ
௫
ଶ
+ 2ܽ
௫
∆ݔ
⎭
ೌ
ሬሬ⃗సೞೌ
ݒ
⃗
,
= ݒ
⃗
,
+ ݒ
⃗
,
(relative motion)
݃ = 9.81
݉
ݏ
ଶ
ൗ
= 32.2 ݂ݐ ݏ
ଶ
⁄
Uniform Circular Motion
_
ܽ
⃗
 =
௩
మ
= ߱
ଶ
ݎ
(centripetal accel)
ݒ = ߱ݎ
(tangential speed)
Dynamics
_
∑ ܨ
⃗
= ݉ܽ
⃗
(Newton’s 2
nd
Law)
ܨ
⃗
,
= −ܨ
⃗
,
(Newton’s 3
rd
Law)
หܨ
⃗
ீ
ห = ݉݃
(near Earth’s surface)
ܨ
⃗
ீ
= −ܩ
భ
మ
మ
ݎ̂
൬
ܩ = 6.67 × 10
ିଵଵ
ܰ݉
ଶ
/݇݃
ଶ
൰
ܨ
⃗
௦
= −݇ݔ⃗
(
Hooke’s Law
)
Friction
_
݂
= ߤ
ܰ
(kinetic)
݂
௦
≤ ߤ
௦
ܰ
(static)
Energy, work, and power
_
ܭ =
1
2
݉ݒ
ଶ
=
ଶ
2݉
∆ܷ
ீ
= ݉݃∆ݕ
(near Earth’s surface)
ܷ
ீ
= −ܩ
భ
మ
(in general)
ܷ
௦
=
1
2
݇ݔ
ଶ
ܹ = න ܨ
⃗
⋅ ݀ݎ⃗
ܹ = ܨ݀
(constant force in
direction of motion)
ܹ
௧
= ∆ܭ
Δܧ = Δܭ + Δܷ = ܹ
ே
ܹ
ீ
=
Ǧ
Δܷ
ீ
ܹ
௦
=
Ǧ
Δܷ
௦
ܲ =
ܹ݀
݀ݐ
ܲ = ܨ
⃗
⋅ ݒ
⃗
ω
2
=
ω
0
2
+
2
α∆θ
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