mechanics

Question 1

Force of gravity between 2 masses

Answer 1

-(G*m₁*m₂/r²)

Question 2

energy of gravity between 2 masses

Answer 2

-(G*m1*m2/r)

Question 3

velocity with acceleration and displacement

Answer 3

v²=v0² + 2*a*Δd

Question 4

distance with initial position, constant velocity and acceleration, and time

Answer 4

x = x0 + v0*t + 0.5*a*t²

Question 5

velocity with acceleration and time

Answer 5

v = v0 + a*t

Question 6

force of friction

Answer 6

F = F_normal*μ

Question 7

centripetal acceleration

Answer 7

a_c = v²/r

Question 8

Torque

Answer 8

τ = F*r*sin(ϴ) ϴ -> angle between position and force vectors

Question 9

momentum

Answer 9

P = m*v

Question 10

impulse

Answer 10

FΔt = ΔP

Question 11

kinetic energy (motion)

Answer 11

KE = 1/2*m*v²

Question 12

gravitational potential energy

Answer 12

U = m*g*h

Question 13

work done on particle in motion with constant force

Answer 13

W = F*Δr*cos(ϴ)

Question 14

Average power

Answer 14

P_avg = W/Δt

Question 15

instantaneous power

Answer 15

P = F*v*cos(ϴ)

Question 16

Force on a spring

Answer 16

F_k = -k*x

Question 17

energy of a spring

Answer 17

U_k = 1/2*k*x²

Question 18

period of a spring

Answer 18

T = 2*π*sqrt(m/k)

Question 19

period of a pendulum

Answer 19

T = 2*π*sqrt(l/g)

Question 20

general period form

Answer 20

T = 1/frequency

Question 21

Linear momentum and angular momentum relationship

Answer 21

p_linear=p_angular/r

Question 22

work-energy principle

Answer 22

Net work is equal to change in kinetic energy

Question 23

Force and potential energy relationship

Answer 23

F_x = -dU/dx

Question 24

elastic collision

Answer 24

total kinetic energy is conserved

Question 25

inelastic collision

Answer 25

momentum is conserved, kinetic energy is not

Question 26

final velocity for perfectly inelastic collision

Answer 26

v_f = (m₁v_1i +m₂v_2i)/(m₁ + m₂)

Question 27

final velocities for elastic collisions

Answer 27

v_1f = [(m₁ - m₂)/(m₁ + m₂)]v_1i + [2m₂/(m₁ + m₂)]v_2i

v_2f = [2m₁/(m₁ + m₂)]v_1i + [(m₂ - m₁)/(m₁ + m₂)]v_2i

Question 28

center of mass for particles

Answer 28

x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂)

Question 29

center of mass for continuous solid

Answer 29

x_cm = (1/M_tot) ∫x(m)dm

Question 30

thrust from rocket

Answer 30

F_thrust = |v_e*dM/dt|

• v_e -> velocity of exhaust*
• dM/dt -> burn rate*

Question 31

arc length

Answer 31

s = rθ

Question 32

rotational kinematic equations

Answer 32

ω_f = ω_i + αt

θ_f = θ_i + ω_it + 1/2αt²

ω_f² = ω_i² + 2α(θ_f - θ_i)

θ_f = θ_i + 1/2(ω_i + ω_f)t

Question 33

Moment of Inertia

Answer 33

I = Σm_ir_i²

Question 34

rotational kinetic energy

Answer 34

K_R = 1/2Iω²

I -> moment of inertia

Question 35

parallel axis theorem

Answer 35

I = I_CM + MD²

D -> distance from center of mass

Question 36

torque

Answer 36

τ = Fd

Question 37

torque and angular acceleration

Answer 37

τ = Iα

Question 38

work-kinetic energy theorem for rotational motion

Answer 38

W = (1/2)Iω_f² - (1/2)Iω_i²

Question 39

angular momentum

Answer 39

L = mvrsinφ

φ -> angle between r and direction of linear momentum (direction of v)

Question 40

angular momentum of rigid object

Answer 40

L = Iω

Question 41

torque on rigid object

Answer 41

τ = Iα

Question 42

Kepler’s first law

Answer 42

all planets move in elliptical orbits with sun at one focus

Question 43

kepler’s second law

Answer 43

the radius vector drawn from sun to a planet sweeps out equal areas in equal time periods

Question 44

kepler’s third law

Answer 44

T² = (4π²/GM_S)a³

• T -> period of rotation*
• a -> semimajor axis*

Question 45

total energy for circular orbits

Answer 45

E = -(GMm)/(2r)

Question 46

total energy for elliptical orbits

Answer 46

E = -(GMm)/(2a)

Question 47

escape velocity

Answer 47

v_esc = √[(2GM_E/R_E)]