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PX148/155 Classical Mechanics & Special Relativity > Circular Motion & Angular Momentum > Flashcards

Circular Motion & Angular Momentum Flashcards

1
Q

Centre of Rotation Definition

A

Point at which particle rotates around. Centre of circle

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2
Q

Plane of Rotation Definition

A

2D plane containing circular path. Eg sheet of paper

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3
Q

Angular Velocity Vector Equation

A
  • v = ω x r
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4
Q

Period Equation

A

P = 2π/ω

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5
Q

Axis of Rotation Definition

A

Line through the centre of rotation and normal to the plane of rotation

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6
Q

For a wheel, when it is rolling or slipping

A
  • Rolling: Tangential Velocity = Linear motion (Static Friction)
  • Slipping: Tangential Velocity ≠ Linear motion (Kinetic Friction)
  • Equation: v_g = v - ωr
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7
Q

Centripetal Acceleration Equation

A

a = (ω^2)r

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8
Q

Torque (moment) equation

A
  • τ = r x F
  • r is the position vector at which the force F is acting on the particle
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9
Q

Angular Momentum Equation

A

L = r x p

“Momentum of momentum”

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10
Q

Torque - Angular Momentum Relation

A

τ = dL/dt

Torque is the rate of change of angular momentum

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11
Q

Moment of Inertia Equation

A

I = mr^2

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11
Q

Angular Momentum - Inertia Relation

A

L = Iω

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12
Q

Moment of Inertia for Rigid Bodies

A
  • I = Σmr^2 = ∫ (r^2) dm
  • Where r is the perpendicular distance from each element to the axis of rotation
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13
Q

Moment of Inertia for a hollow sphere

A
  • I = (2/3)MR^2
  • Axis of rotation through centre
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14
Q

Moment of Inertia for a uniform solid sphere

A
  • I = (2/5)MR^2
  • Axis of rotation through the centre
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15
Q

Moment of Inertia for a thin rod (Centre axis)

A
  • I = (1/12)ML^2
  • Axis of rotation through the centre of the rod
16
Q

Moment of Inertia for a thin rod (End axis)

A

I = (1/3)ML^2

17
Q

Parallel Axis Theorem

A
  • I (Any axis) = I_cm + Md^2
  • where d is the distance between M and the centre
18
Q

Moment of Inertia Kinetic Energy Equation

A

EK = 1/2 I ω^2

PX148/155 Classical Mechanics & Special Relativity (5 decks)

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