9 of 9 ideas
A.4 Rigid body mechanics: 8 ideas
Angular acceleration of a pulley-driven wheel against torque
Research question. How does the torque applied to a bicycle wheel, varied by hanging masses from 20 g to 120 g on a string wound round its axle, affect its angular acceleration?
- A.4 Rigid body mechanics
- HL topic
- Needs care
- Rarely listed
My take. The original is far too broad, so I have cut it to one clean torque against α test, which is much better. Good for HL students who want mechanics with a real intercept meaning; not suitable for SL.
Method, physics and where marks are lost+
- Independent variable
- Hanging mass (20 g to 120 g in 20 g steps, 6 values, three drops each), which sets the tension and hence the torque about the axle.
- What you measure
- Time for the mass to fall a fixed height of about 1.0 m, measured with a phone at 240 fps or light gates. From this the linear acceleration a is found, and angular acceleration α = a/r.
- Controlled variables
- Moment of inertia of the wheel: same wheel, no added masses. Axle radius: measured with vernier calipers. Fall height: fixed with a marked scale. Friction at the bearing: wheel spun and checked before each run, the same bearing used throughout.
- Physics and graph
- τ = Iα, with τ = T r and T = m(g − a). Plot τ (y) against α (x): the gradient is the moment of inertia I and the intercept is the frictional torque. HL only, as rotational dynamics is in A.4.
- SL and HL
- Needs HL content. At HL, get I from the gradient and compare it with a value from the wheel's mass and radius or from a second method such as a swing. Top band: use the intercept for the bearing friction and justify using T = m(g − a) instead of T = mg.
- Where marks are lost
- Research design: the input idea is about force types in general and not measurable, so students who keep it vague get no clear IV. Data analysis: using T = mg, which overestimates torque at large masses. Conclusion: not comparing I with an independent estimate. Evaluation: ignoring string thickness and slipping of the string on the axle.
- Data
- Needs a wheel or turntable on a good axle, string, masses and a timing method; the main uncertainty is the fall time and the bearing friction.
Angular speed change when masses move inward
Research question. How does the starting radius of two 200 g masses on a freely rotating stool, varied from 20 cm to 60 cm, affect the ratio of final to initial angular speed after they are pulled in to 10 cm?
- A.4 Rigid body mechanics
- HL topic
- Needs care
- Rarely listed
My take. A vivid demonstration and worth doing if you have a good bearing. The apparatus inertia correction is what turns it into a strong IA.
Method, physics and where marks are lost+
- Independent variable
- Starting radius of the masses, 20 cm to 60 cm in 10 cm steps (5 values or more, 3 repeats each).
- What you measure
- Angular speed before and after pulling the masses in, from slow motion video with a marked pointer and frame counting. The ratio ωf/ωi is calculated and compared with Ii/If.
- Controlled variables
- Bearing friction: a well oiled turntable and short time between measurements. Final radius: fixed with a stop at 10 cm. Masses: the same pair each time. Starting push: a consistent small initial spin so angular speeds are similar.
- Physics and graph
- Conservation of angular momentum L = Iω when net external torque is negligible. Plot ωf/ωi against Ii/If (calculated from mr²), and expect a line of gradient 1. The apparatus's own moment of inertia adds a constant to each I.
- SL and HL
- This is HL content. Top band work measures the apparatus's own moment of inertia and shows how it changes the predicted ratio, and estimates the angular momentum lost to friction.
- Where marks are lost
- Research design: masses moved unevenly so the axis shifts. Data analysis: reading angular speed by eye instead of from video. Conclusion: not accounting for the moment of inertia of the rotating platform. Evaluation: ignoring friction and the frame rate limit on ω precision.
- Data
- A bicycle wheel or a rotating stool with a phone camera at 120 fps works; the main uncertainty is friction and uneven pulling in.
Mass distribution and speed of rolling cylinders on a ramp
Research question. How does the moment of inertia factor k (I = k m r2, from 0.4 to 1.0 across 6 objects) affect the speed at the bottom of a 1.0 m ramp at 10 degrees?
- A.4 Rigid body mechanics
- HL topic
- Needs care
- Rarely listed
My take. A strong HL option if the graph is linearised properly and k is computed rather than guessed. The twist is to predict v for a new object before testing it.
Method, physics and where marks are lost+
- Independent variable
- Rolling objects of the same radius but different mass distributions: solid cylinder, hollow tube, cylinders filled with sand, water, or with added rings of mass. 6 configurations, 5 runs each. k calculated from the geometry and mass.
- What you measure
- Speed at the bottom from two light gates a short distance apart with a card of known width, or from the time down the ramp with video. v is calculated from distance and time and compared with the theoretical value.
- Controlled variables
- Ramp angle, by measuring height and length with a metre rule. Release point, a stop at the same line each time. Ramp surface, the same board with no slipping. Radius, checked with a calliper for every object.
- Physics and graph
- Energy conservation: m g h = 1/2 m v2 + 1/2 I ω2, with v = ω r, so v2 = 2 g h / (1 + k). Plot v2 against 1 / (1 + k); the gradient is 2 g h, which can be compared with the measured value.
- SL and HL
- Rotational dynamics is HL only. At HL, take the graph to a value of g with uncertainty. Top band: study the effect of slipping, rolling resistance, and the difference between energy loss and the idealised model.
- Where marks are lost
- Research design: varying mass and radius together with the distribution. Data analysis: assuming k for filled objects without calculation. Evaluation: ignoring that the objects may slip or that the light gate measures speed of a section rather than centre of mass.
- Data
- Needs light gates or good video and rollers with known geometry; the main uncertainty is calculating k for partially filled cylinders and rolling friction.
Moment of inertia by torque from a falling mass
Research question. How does the distance of two 100 g masses from the axis, varied from 5 cm to 25 cm in 4 cm steps, affect the moment of inertia of a turntable arm measured by angular acceleration?
- A.4 Rigid body mechanics
- HL topic
- Needs care
- Rarely listed
My take. Excellent HL idea with a clean linearisation and a built-in check on the gradient. Add your own friction calibration to make it stand out.
Method, physics and where marks are lost+
- Independent variable
- Radial distance r of two equal masses on a horizontal rod, 5 cm to 25 cm in 5 steps or more (6 values, 3 repeats).
- What you measure
- A hanging mass on a string wound round the axle gives the torque. Fall time over a measured height, with a stopwatch or video, gives the linear acceleration a, then α = a/R. Moment of inertia I = τ/α, with τ = mR(g − a).
- Controlled variables
- Driving torque: the same hanging mass and axle radius R. Total mass on the rod: masses added symmetrically and never changed. Axle friction: measure it in a run with no added masses and subtract it. Fall height: fixed and measured each time.
- Physics and graph
- τ = Iα and I = Σmr². Plot I against r², the gradient gives the sum of the masses and the intercept gives the apparatus's own moment of inertia. Compare the gradient with 2m = 0.200 kg.
- SL and HL
- Rigid body dynamics is HL only, so this is an HL topic. Depth comes from the intercept analysis, the friction correction and treating the point mass approximation critically for finite sized masses.
- Where marks are lost
- Research design: no way to separate frictional torque. Data analysis: assuming a = g/2 style shortcuts or ignoring string tension. Conclusion: not comparing the gradient with the known mass. Evaluation: not commenting on masses having their own size.
- Data
- A retort stand axle or a low-friction turntable with string, pulley and stopwatch works; short fall times limit precision, so use video analysis.
Moment of inertia of a wheel with movable masses
Research question. How does the radius r of four 50 g masses clamped on a bicycle-style wheel (r = 0.05 to 0.25 m in 5 steps) affect its angular acceleration when a 100 g hanging mass drives it through a string wound on the axle?
- A.4 Rigid body mechanics
- HL topic
- Needs care
- Rarely listed
My take. Good for an HL student who wants real rotational physics with a clean check against the balance. The twist is to build the wheel from something at home, such as a bicycle wheel, and to measure its own bearing friction.
Method, physics and where marks are lost+
- Independent variable
- Radial position r of four equal masses on the wheel spokes or rim slots, 0.05, 0.10, 0.15, 0.20, 0.25 m, each run 5 times.
- What you measure
- Angular acceleration α, found from a video (phone at 120 fps, Tracker) of the falling mass: a from a straight-line fit of distance against t squared, then α = a / axle radius. Moment of inertia then calculated from I = T·R/α.
- Controlled variables
- Driving torque: same hanging mass and same axle radius, checked with a ruler and balance. Total mass on the wheel: same four masses every run. Friction: same axle, tested with no added mass and included as an intercept. Release height: fixed by a marked start line.
- Physics and graph
- τ = Iα with I = I0 + Σ m r². Plot I (or 1/α) against r². The gradient gives the total added mass 4m, which can be checked against the balance, and the intercept gives I0 of the bare wheel. Tension in the string is T = m(g − a), not mg.
- SL and HL
- Rotational dynamics is HL only, so an SL student would need to avoid this or reframe it as energy conservation with a falling mass. At HL, top band work compares the gradient with 4m, deals with axle friction and tension correctly, and tests the parallel axis contribution of masses that are not point-like.
- Where marks are lost
- Research design: torque assumed to equal mg times the axle radius, ignoring that the string tension is lower. Data analysis: friction ignored, leading to a nonzero intercept that is never explained. Conclusion: no comparison of the gradient with the measured masses. Evaluation: uncertainty in release timing not linked to the spread of α.
- Data
- Needs a wheel or turntable on a low friction axle, clamps, a phone camera and Tracker; friction in the bearing is the main uncertainty.
Racing rolling objects down the same ramp
Research question. How does the shape factor k = I/(mr²) of five rolling objects affect their acceleration down a 15° ramp of length 1.20 m?
- A.4 Rigid body mechanics
- HL topic
- Easy data
- Rarely listed
My take. Accessible and testable against a firm prediction. Build your own objects, such as a can with added weights, to make it a personal investigation.
Method, physics and where marks are lost+
- Independent variable
- Object type, giving different k: solid sphere (0.4), solid cylinder (0.5), thin hollow cylinder (1.0), hollow sphere (0.67) and a cylinder with added mass at its rim, five or more values with 5 repeats each.
- What you measure
- Time to travel down a marked 1.20 m with a stopwatch or light gates, giving a = 2s/t². This is compared with the predicted a = g sin θ / (1 + k).
- Controlled variables
- Ramp angle: set from height and length and checked with a protractor. Surface: the same track, so slipping does not happen. Release: from rest at the same mark with a stopper. Ramp length: fixed and measured.
- Physics and graph
- Energy conservation with rotation: mgh = ½mv² + ½Iω² gives a = g sin θ / (1 + k). Plot a against 1/(1+k), the gradient is g sin θ. Mass and radius cancel, which can be tested directly.
- SL and HL
- Rotational kinetic energy belongs to HL rigid body content. For top band, derive the acceleration expression, test whether radius and mass really cancel, and check the no-slip assumption at higher angles.
- Where marks are lost
- Research design: only the standard objects, with no variation in k or angle. Data analysis: comparing only times, not against the model. Conclusion: not commenting on differences between measured and predicted a. Evaluation: ignoring rolling resistance and the hollow objects' wall thickness.
- Data
- A ramp, ruler and stopwatch are enough; light gates or video improve timing, which is the main uncertainty on a 1 to 2 s roll.
Rolling cylinders down a ramp: does radius or mass matter?
Research question. How does the radius of a solid wheel (2.0 cm to 8.0 cm, 6 values) affect its speed at the bottom of a 1.0 m ramp at 10°, with mass fixed?
- A.4 Rigid body mechanics
- HL topic
- Needs care
- Rarely listed
My take. Good HL choice, but reframe it: the physics says mass and radius should not matter, and testing that prediction is the strong version. Twist: use wheels from your own bike or skateboard.
Method, physics and where marks are lost+
- Independent variable
- Radius of a wheel or disc, using 6 discs cut from the same material, or a set of cylinders of different diameter. A separate second run varies mass at fixed radius over 5 values by adding equal masses to the rim or face.
- What you measure
- Time to travel a marked 1.0 m with a light gate pair or video analysis at 240 fps, giving linear speed v, and angular velocity ω = v/r. Five repeats per value.
- Controlled variables
- Ramp angle: fix with a clamp and check with a protractor or from height and length. Release point: mark start line and release without pushing. Surface: same track covering. Mass distribution: keep the shape and material consistent, or state clearly when it is changed.
- Physics and graph
- Conservation of energy with rotation: mgh = ½mv² + ½Iω². For a solid uniform disc, v² = (4/3)gh, independent of mass and radius. Plot v² against h, or acceleration against sin θ, and compare the gradient with 2g/3 sin θ. The interesting result is that mass and radius should have no effect for the same shape.
- SL and HL
- HL only in the full form, because moment of inertia is in A.4. SL students can do a simplified version comparing acceleration with a sliding trolley. Top band: test different shapes (hoop, disc, sphere) and show that the ratio I/mr² decides the speed, not mass or size.
- Where marks are lost
- Research design: the question suggests mass and radius matter, so the hypothesis is wrong and the student never states the predicted null result. Data analysis: slipping treated as rolling. Conclusion: no comparison with the theoretical value. Evaluation: ignoring rolling friction and air resistance.
- Data
- Needs light gates or a phone in slow motion and a rigid ramp; the main uncertainty is release consistency and slipping at low friction.
Wheel radius and the torque to start rotation
Research question. How does the radius of a wheel, from 3.0 cm to 12.0 cm in six steps, affect the torque needed to make it just start turning on a fixed axle when a string wound on its rim is pulled by hanging masses?
- A.4 Rigid body mechanics
- HL topic
- Needs care
- Rarely listed
My take. Only HL and the original question hides a trap, since the torque needed to beat friction hardly depends on radius. Rewrite it as the angular acceleration under a fixed torque and it becomes a solid investigation.
Method, physics and where marks are lost+
- Independent variable
- Radius of the rim on which the string acts, 6 values from 3.0 to 12.0 cm, using stacked discs of different radii on one axle, each repeated 5 times.
- What you measure
- Mass added to a hanger until the wheel starts to turn, weighed on a balance. Torque is calculated as τ = mgr. Alternatively use a newton meter for the pull.
- Controlled variables
- Axle friction: same bearing, lubricated equally and checked with the wheel unloaded. Wheel mass and inertia: same stack of discs, only the string radius changes. String angle: kept tangent and horizontal with a pulley. Starting position: marked on the rim.
- Physics and graph
- τ = Fr. If friction at the axle is constant the torque to overcome it is constant, so the mass needed is proportional to 1/r. Plot m against 1/r. The gradient gives the friction torque divided by g. A better version measures angular acceleration for a fixed hanging mass and uses τ = Iα.
- SL and HL
- The syllabus content sits in HL topic A.4, so this is an HL idea. Top band work finds the friction torque from the intercept, and repeats with a timed release to get α and I.
- Where marks are lost
- Research design: it is unclear what is meant by torque required, so the method measures something loose. Data analysis: no uncertainty from the stiction threshold. Conclusion: expecting torque to grow with r when it is really constant against friction. Evaluation: not addressing the axle friction as a systematic effect.
- Data
- Simple kit with a balance and stand, but the starting threshold is a judgement call, so the main uncertainty is the repeatability of stiction.
A.5 Galilean and special relativity: 1 idea
Cosmic ray muon counts at two altitudes and time dilation
Research question. Does the observed fraction of atmospheric muons surviving from high altitude to sea level agree better with relativistic time dilation or with classical decay, given a mean muon lifetime of 2.2 microseconds?
- A.5 Galilean and special relativity
- HL topic
- Hard data
- database
- Rarely listed
My take. Ambitious and hard to make clean with only secondary data. Consider a cosmic ray detector from a university outreach programme if your school has access, otherwise pick something simpler.
Method, physics and where marks are lost+
- Independent variable
- Altitude of the detector, using at least two published sites, or 5 or more altitudes if the dataset allows.
- What you measure
- Muon flux from published counts at each altitude; survival fraction is the ratio of fluxes, compared with exp(-t/τ) and exp(-t/(γ τ)).
- Controlled variables
- Same muon energy or momentum band across datasets. Same detector type and angle to the vertical. Comparable atmospheric conditions. Same production height assumed in both predictions.
- Physics and graph
- Time dilation t = γ t0 and exponential decay N = N0 exp(-t/τ). Plot ln(N/N0) against altitude, and compare the gradient with the classical and relativistic predictions.
- SL and HL
- Relativity is HL only, so this is an HL idea. Top band: propagate uncertainties in flux and production height, and note energy loss in the atmosphere.
- Where marks are lost
- Research design: mixing datasets with different energy cuts. Data analysis: no uncertainty on flux. Conclusion: overclaiming from two points. Evaluation: ignoring the spread in production height and muon energy.
- Data
- Needs published flux data at known altitudes, which is hard to match in energy range; the uncertainty in production height and speed dominates.
Ideas were collected from public lists and published IA titles, merged when they are the same investigation, and rewritten from scratch. “On N sites” counts how many public lists carry the same investigation. How this list was made.
Frequently asked questions
What are good IB Physics IA ideas on rigid body mechanics and relativity?
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Good starting points with easy data that few sites list are racing rolling objects down the same ramp. Each one gives a straight-line graph from school equipment, which is what the Data analysis and Conclusion criteria need.
Which rigid body mechanics and relativity IA ideas are overdone?
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None of the 9 ideas on this page appears on three or more public lists, so any of them is less likely to look like a copy.
Can I do a rigid body mechanics and relativity IA at SL?
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0 of the 9 ideas use SL physics. The others rely on HL-only content and are marked as HL topics.