Formulae for PHYS 1410 Final Exam Spring 2017 (side 1)

Graphical Analysis

avg

rv

t

(slope of position versus time) f ir r r f it t t

avg

va

t

(slope of velocity versus time)

inst

drv

dt

(slope of position versus time at a specific time)

2

2inst

dv d ra

dt dt (slope of velocity versus time at a specific time)

Sf = Si + area under velocity versus time for Δt = tf - ti

Vfs = Vis + area under acceleration versus time for Δt = tf - ti

Analytical Analysis (for constant linear acceleration)

21

2f i iS SS S v t a t

fS iS Sv v a t

2 2 2fS iS Sv v a S

Formulae for PHYS 1410 Final Exam Spring 2017 (side 2)

Graphical Analysis

avgt

(slope of angular position versus time)

avgt

(slope of angular velocity versus time)

inst

d

dt

(slope of angular position versus time at a specific time)

2

2inst

d d

dt dt

(slope of angular velocity versus time at a specific time)

Ɵf = Ɵi + area under angular velocity versus time for Δt = tf - ti

ωfs = ωis + area under angular acceleration versus time for Δt = tf - ti

Analytical Analysis (for constant angular acceleration)

21

2f i i t t

f i t

2 2 2f i

s r

v r

ta r

22

r

va r

r

Formulae for PHYS 1410 Final Exam Spring 2017 (side 3)

Work and Kinetic Energy:

f

i

s

F aves

W F ds F s area under curve

FW F r (constant force)

221

2 2

pK mv

m netK W

Potential Energy:

gU mgy 21

( )2

sU k s ( )sp sF k s

With conservative forces only: With non-conservative forces:

f f i iK U K U i i ext f f thK U W K U E

Power:

sysdEP

dt

P F v

Impulse and linear momentum:

p mv

dpF

dt

aveJ Fdt F t area under curve p J

Elastic collision f iP P and f iK K

Moment of Inertia: Torque:

2

i i

i

I m r si  nrF r F rF

Disk: 𝐼𝐷 = 1

2 𝑀𝑅2

r F

Hoop: 𝐼𝐻𝑜𝑜𝑝 = 𝑀𝑅2

netnet

I

Solid Sphere: 𝐼𝑆𝑜𝑙𝑖𝑑𝑆𝑝ℎ𝑒𝑟𝑒 = 2

5 𝑀𝑅2

Hollow Sphere: 𝐼𝐻𝑜𝑙𝑙𝑜𝑤𝑆𝑝ℎ𝑒𝑟𝑒 = 2

3 𝑀𝑅2

Kinetic Energy of rotation: 21

2rotK I

Angular Momentum: L I net

dL

dt

Gravitation: 1 2

2

Gm mF

r

G = 6.67 x 10-11 N m2/kg2

2surface

GMg

R

22 34

T rGM

Oscillations and Simple Harmonic Motion:

( )sp xF k x 2k

fm

1

fT

( ) cos( )ox t A t

max( ) sin( ) sin( )x o ov t A t v t

2( ) cos( )x oa t A t

2g

fL

simple pendulum