Theme A — Space, Time and Motion
A.4.8 Angular Impulse — IB Physics HL Revision Notes & Topical Questions
5 min read 8 parts Lesson 50 of 63 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
A.4.8 Angular Impulse — IB PHYSICS HL notes: Define angular impulse and relate it to change in angular momentum, including from torque–time graphs.Resultant force = rate of change of linear momentum — F = Δp/Δt.What the symbols mean: F = force (N) · Δt = time the force acts (s) ·…
- Linear impulse
- Resultant torque
- The area under a torque–time graph
- For a changing torque, use the area
- Areas above the axis are positive and below are negative
- Take anticlockwise as positive
Part 1 of 6Linear impulse revisited
Resultant force
Resultant force rate of change of linear momentum — F = Δp/Δt.
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)
Linear impulse
- FΔt = Δp = Δ(mv).
Part 2 of 6Rotational analogue
Resultant torque
Resultant torque rate of change of angular momentum — τ = ΔL/Δt.
Angular impulse
Angular impulse an average resultant torque τ acting for a time Δt produces a change ΔL in angular momentum.
- ΔL = τΔt = Δ(Iω)
Unit
- Unit kg m2 s-1, or N m s.
A small torque for a long time has the same effect as a large torque for a short time.
Part 3 of 6Torque–time graphs
1The area under a torque–time graph
The area under a torque–time graph angular impulse = change in angular momentum.
2For a changing torque, use the area
- For a changing torque, use the area or an average torque.
3Areas above the axis are positive and below are negative
- Areas above the axis are positive and below are negative in the chosen sense of rotation.
4
Use triangles and rectangles to find the area.
Part 4 of 6Finding the final angular velocity
Finding the final angular velocity
Find the angular impulse from the area under the τ–t graph.
Write ΔL = I(ωf − ωi).
Substitute I, ωi (with its sign) and solve for ωf.
1Take anticlockwise as positive
- Take anticlockwise as positive and a clockwise initial rotation as negative.
2
Example: impulse of +15 N m s then −10 N m s gives +5 N m s, which changes ω by +1.0 rad s-1 when I = 5.0 kg m2.
Part 5 of 6Limitations
1The equation ΔL
τΔt needs a constant resultant torque.
2
If the torque changes, use the area under the graph or an average value.
3
Angular impulse describes the effect of a torque over a time interval.
4It links to conservation of angular momentum
- It links to conservation of angular momentum zero torque gives zero angular impulse.
Part 6 of 6More from the specification
More from the specification
Angular momentum change from torque impulses
- Angular momentum change from torque impulses integrating applied rotational torque over time yields angular impulse delivered to a spinning rotor system.
Angular Impulse and Momentum
- Angular impulse is the product of net torque and time duration,
- (Delta L = tau * Delta t)
- which equals the change in angular momentum of a rotating object.
- (Delta L = I * Delta omega)
Moment of Inertia
- The moment of inertia I measures an object's resistance to rotational acceleration, depending on its total mass and the square of mass distribution distance from the rotational axis.
- (I = Sigma m * r2
Torque from a Couple
- A couple consists of two parallel forces of equal magnitude directed in opposite directions separated by a perpendicular distance, creating a net turning effect without translating the center of mass.
Rotational Kinematics Analogy
- Rotational motion equations parallel linear motion: angular displacement theta, angular velocity omega,
- and angular acceleration alpha correspond directly to linear displacement s, velocity v,
- and acceleration a.
Perpendicular
- At right angles.
Radius
- Distance from the centre to the circular path.
Kinetic energy
- K = ½mv2, energy of motion.
Perpendicular distance
- Distance from the axis to the line of motion, r⊥ = r sinθ.
Velocity
- Rate of change of displacement.
Inertia
- Resistance of an object to changes in its motion.
Acceleration
- Rate of change of velocity.
Distance
- Total length of path travelled, a scalar.
Displacement
- Change in position.
Couple
- A pair of equal opposite forces with different lines of action.
Equilibrium
- State with zero net force.
Newton
- Unit of force, kg m s-2.
Key terms
| Term | Meaning |
|---|---|
| Angular impulse | Torque multiplied by time, equal to change in angular momentum. |
| Torque–time graph | Graph whose area gives angular impulse. |
| Angular momentum | L = Iω. |
| Net torque | Resultant torque on a body. |
| Clockwise | Direction of rotation, taken negative in the example. |
| Change in angular momentum | Final L minus initial L. |
Avoid these mistakes
1
Forgetting the sign of the angular impulse when the torque reverses.
2
Using ΔL = τΔt with a changing torque without an average.
3
Ignoring the initial angular velocity.
4
Confusing angular impulse with torque.
5
Using the wrong units — kg m2 s-1 or N m s.
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