Theme A — Space, Time and Motion
A.4.2 Rotational Equilibrium — IB Physics HL Revision Notes & Topical Questions
5 min read 8 parts Lesson 44 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.4.2 Rotational Equilibrium — IB PHYSICS HL notes: State the conditions for rotational equilibrium and apply the principle of moments to beams.Rotational equilibrium = zero resultant torque on a body.A body in rotational equilibrium stays at rest or rotates with constant angular…
- Sum of clockwise torques
- Torque of each force τ
- Choose a point through which unknown forces act
- A resultant torque causes angular acceleration
- Net torque
- Displacement
Part 1 of 6Rotational equilibrium
Rotational equilibrium
Rotational equilibrium zero resultant torque on a body.
A body in rotational equilibrium stays at rest or rotates with constant angular velocity.
It is the rotational analogue of Newton's first law for translational equilibrium.
A rigid extended body, such as a beam, can be in rotational equilibrium.
Part 2 of 6Principle of moments
Sum of clockwise torques
Sum of clockwise torques sum of anticlockwise torques.
Torque of each force τ
Fr sin θ, and τ = Fr when the force is perpendicular.
Balanced forces either side of a pivot give a beam with zero resultant torque.
Both conditions are needed for full equilibrium.
- Zero resultant force for translational equilibrium.
- Zero resultant torque for rotational equilibrium.
Part 3 of 6Choosing the pivot point
1
Any point can be used, not just the axis of rotation.
2Choose a point through which unknown forces act
- Choose a point through which unknown forces act their torque is zero and they drop out.
3
Choose a point where the torque of most forces is known.
4
The weight of a uniform beam acts at its centre.
Part 4 of 6Unbalanced torque
Unbalanced torque
A resultant torque causes angular acceleration
- A resultant torque causes angular acceleration like a resultant force causes linear acceleration.
The direction of the angular acceleration is the direction of the net torque.
A beam with more clockwise than anticlockwise torque rotates clockwise with increasing angular speed.
Part 5 of 6Tipping and limiting conditions
1
A plank just about to tip has the support force at one support equal to zero.
2
At that point take torques about the other support.
3
Method.
- Identify all forces and which pivot to use.
- Write the clockwise and anticlockwise torques about it.
- Equate them and solve for the unknown distance or force.
4
Torque is a vector, but only its clockwise or anticlockwise sense is needed at this level.
Part 6 of 6More from the specification
More from the specification
Static equilibrium in a rotating system
- Static equilibrium in a rotating system vanishing resultant forces and zero net torque ensure static mechanical equilibrium within a rigid body system.
Conditions for Rotational Equilibrium
- A rigid body is in complete rotational equilibrium when the vector sum of all external torques acting about any arbitrary axis equals zero (sigma_tau = 0), preventing angular acceleration.
Torque of a Couple
- A couple consists of two parallel forces of equal magnitude acting in opposite directions along parallel lines;
- its resultant torque is independent of pivot position and equals force multiplied by perpendicular separation: tau = F d.
Moment of Inertia and Angular Acceleration
- Moment of inertia (I) quantifies rotational inertia;
- an applied net torque produces an angular acceleration alpha according to the rotational analogue of Newton's second law: tau = I alpha.
Rotational Kinetic Energy and Work Done
- A spinning object possesses rotational kinetic energy Ek_rot = 1/2 I omega2;
- the work done by a net torque during an angular displacement delta_theta is given by W = tau delta_theta.
Kinetic energy
- K = ½mv2, energy of motion.
Inertia
- Resistance of an object to changes in its motion.
Displacement
- Change in position.
Couple
- A pair of equal opposite forces with different lines of action.
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.
Key terms
| Term | Meaning |
|---|---|
| Rotational equilibrium | Zero resultant torque. |
| Principle of moments | Clockwise torques equal anticlockwise torques at equilibrium. |
| Pivot | Point about which torques are calculated. |
| Beam | Rigid extended body, often supported at points. |
| Net torque | Resultant torque on a body. |
| Angular acceleration | Rate of change of angular velocity. |
Avoid these mistakes
1
Using only the force balance and forgetting the torque balance.
2
Measuring distances from the wrong pivot for different forces.
3
Forgetting the weight of the beam, which acts at its centre.
4
Using non-perpendicular distances without a sine factor.
5
Treating zero net torque as meaning the body must be at rest.
Marked practiceQuizzes for this lesson
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