Formulae

Question 1

Average Velocity?

Instantaneous velocity?

Answer 1

Average = Δs/t

Instant = gradient of displacement-time graph

Question 2

Average acceleration?

Instantaneous acceleration?

Answer 2

Average = Δv/t

Instant = gradient of velocity-time graph

Question 3

Average angular velocity?
Instantaneous angular velocity?
Units?

Answer 3

Average: ω=Δθ/t

Instant = gradient of angle-time graph

Unit = rad s⁻¹

Question 4

Average angular acceleration?
Instantaneous angular acceleration?
Units?

Answer 4

Average: α=Δω/t

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

Units = rad s⁻²

Question 5

Weight?

Unit?

Answer 5

W=mg

Unit = N (kg m s⁻²)

Question 6

Coefficient of friction?

Unit?

Answer 6

µ=F/N

No units since it is a ratio

Question 7

Pressure?

Unit?

Answer 7

p=F/A

Unit = N m⁻²

Question 8

Unbalanced force?

Answer 8

F=ma

Question 9

Momentum?

Units?

Answer 9

p=mv

Units = N s

Question 10

4 equations of linear motion?

Answer 10

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

Question 11

4 equations of angular motion?

Answer 11

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

Question 12

Moment?

Units?

Answer 12

M=Fd

Units = N m

Question 13

Mechanical advantage?

Units?

Answer 13

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

No units since it is a ratio

Question 14

Tangential linear velocity?

Answer 14

v=rω

Question 15

Tangential linear acceleration?

Answer 15

at=rα

Question 16

Radial linear acceleration?

Answer 16

ar = v²/t = rω²

Question 17

Angular torque?

Answer 17

M=Iα

Question 18

Moment of inertia?

Units?

Answer 18

I=mk²

Units = kg m²

Question 19

General radius of gyration?

Answer 19

k=√(I/m)

Question 20

Radius of gyration of a solid ring or spoked wheel?

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

Answer 20

k=r

k=1/2r²

Question 21

Angular momentum?

Units?

Answer 21

L=Iω

Units = kg m² rad s⁻¹

Question 22

Work?

Units?

Answer 22

w=Fd (force x distance)

Units = J

Question 23

Power?

Units?

Answer 23

P=w/t

Units = W (J s⁻¹)

Question 24

Linear kinetic energy?

Units?

Answer 24

KE = 1/2mv²

Units = J

Question 25

Rotational kinetic energy? | Units?

Answer 25

KE = 1/2Iω² Units = J

Question 26

Potential energy? | Units?

Answer 26

PE = mgh OR PE = Wh Units = J

Question 27

Axial stress? | Units?

Answer 27

σ=F/A Units = Pa (N m⁻²)

Question 28

Axial strain?

Answer 28

ε=ΔL/L

Question 29

Young's Modulus? | Units?

Answer 29

E=σ/ε Units = Pa

Question 30

Rigidity? | Units?

Answer 30

Rigidity = EA Units = N

Question 31

Stiffness? | Units?

Answer 31

k = F/ΔL = EA/L Units = N m⁻¹

Question 32

Flexibility? | Units?

Answer 32

f = 1/k = ΔL/F = L/EA Units = m N⁻¹

Question 33

Strain rate?

Answer 33

Strain rate = Δε/Δt

Question 34

Coefficient of viscosity? | Units?

Answer 34

η = σ/strain rate units = Nm⁻² .s (Pa .s)

Question 35

Shear stress? | Units?

Answer 35

τ = V/A Units = Pa

Question 36

Shear strain? | Units?

Answer 36

``` ϕ = angle sheared = x/d (x = distance sheared; d = distance between 2 shearing forces) ``` Units = rad

Question 37

Shear strength?

Answer 37

V required to break/A

Question 38

Modulus of Rigidity? | Unit?

Answer 38

G = τ/ϕ Unit = Pa

Question 39

Variation in stress in layers of a bending beam?

Answer 39

σ = εE = yE/r

Question 40

Bending moment?

Answer 40

M = Fd (same as normal moment)

Question 41

Maximum bending moment?

Answer 41

Mmax = σI/ymax

Question 42

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

Answer 42

M/I = σ/y = E/R | MISYER

Question 43

Second moment of area of a rectangular bar? | ymax of a rectangular bar?

Answer 43

I = bd³/12 ymax = d/2

Question 44

Second moment of area of a solid circular bar? | ymax of a solid circular bar?

Answer 44

I = πd⁴/64 ymax = d/2

Question 45

Second moment of area of a hollow circular bar? | ymax of a hollow circular bar?

Answer 45

I = π(D⁴-d⁴)/64 ymax = D/2

Question 46

Shear stress in torsion? | Units?

Answer 46

τ = Gθr/L OR τ = Gϕ θ = angle of twist in RADIANS

Question 47

Shear strain in torsion?

Answer 47

τ = θr/L Unit = rad (θ = angle sheared in RADIANS)

Question 48

Twisting moment?

Answer 48

M = JGθ/L

Question 49

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

Answer 49

M/J = τ/r = Gθ/L

Question 50

Polar second moment of area of a solid circular bar? | Units?

Answer 50

J = πd⁴/32 Units = m⁴

Question 51

Polar second moment of area of a hollow circular bar? | Units?

Answer 51

J = π(D⁴-d⁴)/32 Units = m⁴

Question 52

Density? | Units?

Answer 52

ρ = mv Units = kg m⁻³