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BMSc Orthopaedic Module > Formulae > Flashcards

Formulae Flashcards

1
Q

Average Velocity?

Instantaneous velocity?

A

Average = Δs/t

Instant = gradient of displacement-time graph

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2
Q

Average acceleration?

Instantaneous acceleration?

A

Average = Δv/t

Instant = gradient of velocity-time graph

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3
Q

Average angular velocity?
Instantaneous angular velocity?
Units?

A

Average: ω=Δθ/t

Instant = gradient of angle-time graph

Unit = rad s⁻¹

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4
Q

Average angular acceleration?
Instantaneous angular acceleration?
Units?

A

Average: α=Δω/t

Instantaneous = gradient of tangent to curve of angle-time graph

Units = rad s⁻²

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5
Q

Weight?

Unit?

A

W=mg

Unit = N (kg m s⁻²)

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6
Q

Coefficient of friction?

Unit?

A

µ=F/N

No units since it is a ratio

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7
Q

Pressure?

Unit?

A

p=F/A

Unit = N m⁻²

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8
Q

Unbalanced force?

A

F=ma

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9
Q

Momentum?

Units?

A

p=mv

Units = N s

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10
Q

4 equations of linear motion?

A 
v = u+at
s = 1/2(u+v)t
v² = u²+2as
s = ut+1/2at²
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11
Q

4 equations of angular motion?

A 
ω = ω₀+αt
θ = 1/2(ω₀+ω)t
ω² = ω₀+2αθ
θ = ω₀t+1/2αt²
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12
Q

Moment?

Units?

A

M=Fd

Units = N m

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13
Q

Mechanical advantage?

Units?

A

MA = dₑ/dᵣ (effort arm/resistance arm)

No units since it is a ratio

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14
Q

Tangential linear velocity?

A

v=rω

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15
Q

Tangential linear acceleration?

A

at=rα

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16
Q

Radial linear acceleration?

A

ar = v²/t = rω²

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17
Q

Angular torque?

A

M=Iα

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18
Q

Moment of inertia?

Units?

A

I=mk²

Units = kg m²

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19
Q

General radius of gyration?

A

k=√(I/m)

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20
Q

Radius of gyration of a solid ring or spoked wheel?

Of a solid disc (e.g. a flywheel)?

A

k=r

k=1/2r²

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21
Q

Angular momentum?

Units?

A

L=Iω

Units = kg m² rad s⁻¹

22
Q

Work?

Units?

A

w=Fd (force x distance)

Units = J

23
Q

Power?

Units?

A

P=w/t

Units = W (J s⁻¹)

24
Q

Linear kinetic energy?

Units?

A

KE = 1/2mv²

Units = J

25
Q

Rotational kinetic energy?

Units?

A

KE = 1/2Iω²

Units = J

26
Q

Potential energy?

Units?

A

PE = mgh

OR

PE = Wh

Units = J

27
Q

Axial stress?

Units?

A

σ=F/A

Units = Pa (N m⁻²)

28
Q

Axial strain?

A

ε=ΔL/L

29
Q

Young’s Modulus?

Units?

A

E=σ/ε

Units = Pa

30
Q

Rigidity?

Units?

A

Rigidity = EA

Units = N

31
Q

Stiffness?

Units?

A

k = F/ΔL = EA/L

Units = N m⁻¹

32
Q

Flexibility?

Units?

A

f = 1/k = ΔL/F = L/EA

Units = m N⁻¹

33
Q

Strain rate?

A

Strain rate = Δε/Δt

34
Q

Coefficient of viscosity?

Units?

A

η = σ/strain rate

units = Nm⁻² .s (Pa .s)

35
Q

Shear stress?

Units?

A

τ = V/A

Units = Pa

36
Q

Shear strain?

Units?

A 
ϕ = angle sheared = x/d
(x = distance sheared; d = distance between 2 shearing forces)

Units = rad

37
Q

Shear strength?

A

V required to break/A

38
Q

Modulus of Rigidity?

Unit?

A

G = τ/ϕ

Unit = Pa

39
Q

Variation in stress in layers of a bending beam?

A

σ = εE = yE/r

40
Q

Bending moment?

A

M = Fd (same as normal moment)

41
Q

Maximum bending moment?

A

Mmax = σI/ymax

42
Q

Relationship between variation in stress if a bent beam and maximum bending moment?

A

M/I = σ/y = E/R

MISYER

43
Q

Second moment of area of a rectangular bar?

ymax of a rectangular bar?

A

I = bd³/12

ymax = d/2

44
Q

Second moment of area of a solid circular bar?

ymax of a solid circular bar?

A

I = πd⁴/64

ymax = d/2

45
Q

Second moment of area of a hollow circular bar?

ymax of a hollow circular bar?

A

I = π(D⁴-d⁴)/64

ymax = D/2

46
Q

Shear stress in torsion?

Units?

A

τ = Gθr/L
OR
τ = Gϕ

θ = angle of twist in RADIANS

47
Q

Shear strain in torsion?

A

τ = θr/L

Unit = rad

(θ = angle sheared in RADIANS)

48
Q

Twisting moment?

A

M = JGθ/L

49
Q

Relationship between twisting moment, shear strain and shear stress in torsion?

A

M/J = τ/r = Gθ/L

50
Q

Polar second moment of area of a solid circular bar?

Units?

A

J = πd⁴/32

Units = m⁴

51
Q

Polar second moment of area of a hollow circular bar?

Units?

A

J = π(D⁴-d⁴)/32

Units = m⁴

52
Q

Density?

Units?

A

ρ = mv

Units = kg m⁻³

BMSc Orthopaedic Module (14 decks)

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