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Theme A — Space, Time and Motion

A.4.4 Angular Acceleration Formula — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 46 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Lesson summary

A.4.4 Angular Acceleration Formula — IB PHYSICS HL notes: Use the four rotational kinematic equations for uniform angular acceleration.The four linear equations for uniform acceleration have rotational equivalents.Linear: v = u + at, s = ut + ½at2, v2 = u2 + 2as, s = ½(u + v)t.Wh…

  • What the symbols mean
  • Swap the five linear variables for rotational ones
  • They apply only to constant angular acceleration
  • A turntable stopping
  • Number of rotations
  • Check units

Part 1 of 6From linear to rotational equations

From linear to rotational equations
The four linear equations for uniform acceleration have rotational equivalents.
Linear: v
Linear: v u + at, s = ut + ½at2, v2 = u2 + 2as, s = ½(u + v)t.
What the symbols mean: v = final velocity (m s−1) · u = initial velocity (m s−1) · a = acceleration (m s−2) · t = time (s)
Swap the five linear variables for rotational ones
  • Swap the five linear variables for rotational ones s to θ, u to ωi, v to ωf, a to α, t unchanged.

Part 2 of 6The four equations

The four equations
ωf
ωi + αt
θ
ωit + ½αt2
ωf2
ωi2 + 2αθ
θ
½(ωi + ωf)t
They apply only to constant angular acceleration
  • They apply only to constant angular acceleration just as suvat needs constant linear acceleration.

Part 3 of 6Variable table

VariableLinearRotational
Displacementsθ
Initial velocityuωi
Final velocityvωf
Accelerationaα
Timett

Part 4 of 6Choosing an equation

Choosing an equation
List the known and unknown rotational variables with signs.
Pick the equation containing them and not the unwanted variable.
Rearrange and substitute with angles in radians.
A turntable stopping
  • A turntable stopping use ωf2 = ωi2 + 2αθ with ωf = 0.
Choose a positive direction (clockwise or anticlockwise) and use it for θ, ω and α.

Part 5 of 6Counting rotations

One full rotation is 2π radians.
Number of rotations
θ/2π.
Convert revolutions per minute to rad s-1 by multiplying by 2π/60.
Check units
  • Check units angles in radians, time in seconds.

Part 6 of 6More from the specification

More from the specification
Angular kinematic acceleration relations
  • Angular kinematic acceleration relations dividing net external torque by rotational inertia determines angular acceleration of a rotating rigid body system.
Angular acceleration
  • Angular acceleration rate of change of angular velocity, found from torque divided by moment of inertia
Torque
  • Torque force times perpendicular distance from the axis, the rotational equivalent of force
Moment of inertia
  • Moment of inertia a measure of resistance to angular acceleration that depends on the mass distribution
Angular momentum
  • Angular momentum moment of inertia times angular velocity, conserved when the resultant external torque is zero
Equilibrium
  • State with zero net force.
Perpendicular
  • At right angles.
Impulse
  • J = FΔt = Δp.
    What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
Radius
  • Distance from the centre to the circular path.
Rotational equilibrium
  • Στ = 0; no angular acceleration.
Angular impulse
  • Product of net torque and the time it acts, τΔt.
Kinetic energy
  • K = ½mv2, energy of motion.
Perpendicular distance
  • Distance from the axis to the line of motion, r⊥ = r sinθ.
Torque
  • Rotational effect of a force, τ = rF sinθ.
Moment
  • Turning effect of a force.
Inertia
  • Resistance of an object to changes in its motion.
Momentum
  • P = mv, a vector.
Resultant
  • Vector sum of two or more vectors.
Force
  • A push or pull measured in newtons.
Distance
  • Total length of path travelled, a scalar.
Couple
  • A pair of equal opposite forces with different lines of action.

Key terms

TermMeaning
Uniform angular accelerationAngular acceleration constant in magnitude and direction.
Rotational kinematic equationsEquations linking θ, ω_i, ω_f, α and t.
Angular displacementChange in angle in radians.
RevolutionOne full turn, 2π radians.
Initial angular velocityAngular velocity at the start, ω_i.
Final angular velocityAngular velocity at the end, ω_f.

Avoid these mistakes

1
Using degrees in the equations — use radians.
2
Applying the equations when angular acceleration is not constant.
3
Forgetting the sign of α for a slowing body.
4
Mixing linear and angular variables in one equation.
5
Forgetting to divide θ by 2π to count rotations.

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