What does Rigid Body Mechanics cover in IB Physics?

This topic extends linear motion concepts to rotational motion, focusing on torques, angular kinematics, and angular momentum for rigid bodies. Torque tau = Fr sin θ causes angular acceleration α, related by Newton's second law for rotation tau = Iα. Rotational motion is described by angular displacement Δθ, angular velocity ω, and angular acceleration α.

Is Rigid Body Mechanics SL or HL?

Rigid Body Mechanics is HL only. SL students are not examined on it.

How does FourtyFive help me practise Rigid Body Mechanics?

FourtyFive has 25 Rigid Body Mechanics questions. Every answer you write is marked mark by mark, IB-style, and you see where each mark was won or lost. Every part has a hint, the AI tutor helps you through the step you are stuck on, and your Study Profile picks what to practise next.

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Topic A.4 · HL only

Rigid Body Mechanics: notes and practice questions

Q: How do I revise Rigid Body Mechanics for IB Physics?

Start from the core idea: this topic extends linear motion concepts to rotational motion, focusing on torques, angular kinematics, and angular momentum for rigid bodies. In the exam: hL Paper 1A and HL Paper 2 only. Typical shapes are a rotational-equilibrium calculation, a "coupled bodies" angular momentum conservation problem, and a rolling-without-slipping energy split. Then practise exam-style questions, easiest first, writing out every step of your working before you check it.

8 min read Jump to 20 practice questions

Summary

This topic extends linear motion concepts to rotational motion, focusing on torques, angular kinematics, and angular momentum for rigid bodies.
Torque $\tau = Fr \sin \theta$ causes angular acceleration $\alpha$ , related by Newton's second law for rotation $\tau = I\alpha$ .
Rotational motion is described by angular displacement $\Delta\theta$ , angular velocity $\omega$ , and angular acceleration $\alpha$ .
Equations for uniform angular acceleration are analogous to linear kinematics.
Moment of inertia $I$ depends on mass distribution, with $I = \sum mr^2$ for a system of point masses.
Angular momentum $L = I\omega$ is conserved if no resultant external torque acts on the system.
Rotational kinetic energy is given by $E_k = \frac{1}{2}I\omega^2$ .

How it is examined

HL Paper 1A and HL Paper 2 only. Typical shapes are a rotational-equilibrium calculation, a "coupled bodies" angular momentum conservation problem, and a rolling-without-slipping energy split. Command terms: determine, show, calculate, explain. If a question needs a moment of inertia formula, the formula belongs in the stem.

Given in the booklet

All four rotational equations of motion, $\tau = Fr\sin\theta$ , $I = \Sigma m r^2$ , $\tau = I\alpha$ , $L = I\omega$ , $\Delta L = \tau\Delta t = \Delta(I\omega)$ , $E_\text{k} = \tfrac{1}{2}I\omega^2 = L^2/2I$ . Moments of inertia of standard shapes (disc, hoop, rod, sphere) are not in the booklet: the guidance says the equation "will be provided when necessary", meaning in the question stem. A generated question must supply it too.

Key ideas

There is no standard level content in A.4.

Not assessed

A calculation of the centre of mass of bodies is not required; there should be an understanding that when considering linear motion, the mass of an extended body may be taken as concentrated at the centre of mass.
The term angular velocity will be used although a formal vector treatment is not required.

Guiding questions

How can the understanding of linear motion be applied to rotational motion?
How is the understanding of the torques acting on a system used to predict changes in rotational motion?
How does the distribution of mass within a body affect its rotational motion?

Linking questions

How does rotation apply to the motion of charged particles or satellites in orbit?
How does conservation of angular momentum lead to the determination of the Bohr radius?
How does a torque lead to simple harmonic motion?
How are the laws of conservation and equations of motion in the context of rotational motion analogous to those governing linear motion?
How can rotation lead to the generation of an electric current?

Practice questions

25 questions · 3 easy · 21 medium · 1 hard

Showing 20 of 20

Question 1

EasyPaper 1A · calculator1 mark

What is the SI base unit of moment of inertia?

A. $\text{kg m}$

B. $\text{kg m}^2$

C. $\text{kg m s}^{-1}$

D. $\text{kg m}^{-2}$

Question 2

MediumPaper 1A · calculator1 mark

A potter's wheel with a moment of inertia of 8.0 kg m $^2$ is rotating freely with an angular speed of 20 rad s $^{-1}$ . The potter applies a gentle braking force, slowing the wheel to an angular speed of 5.0 rad s $^{-1}$ .

What is the magnitude of the angular impulse exerted on the wheel?

A. 40 kg m $^2$ s $^{-1}$

B. 120 kg m $^2$ s $^{-1}$

C. 160 kg m $^2$ s $^{-1}$

D. 200 kg m $^2$ s $^{-1}$

Question 3

HardPaper 2 · calculator9 marks

(a)

A large potter's wheel, with a moment of inertia of $1.2 \text{ kg m}^2$ , is initially at rest. A motor uniformly accelerates it to an angular speed of $7.0 \text{ rad s}^{-1}$ in $5.0 \text{ s}$ .

(a) Calculate the resultant torque acting on the potter's wheel during this acceleration.

[3]

(b)

(b) Calculate the rotational kinetic energy of the potter's wheel when it reaches an angular speed of $7.0 \text{ rad s}^{-1}$ .

[2]

(c)

(c) The potter's wheel has a radius of $20 \text{ cm}$ . After the motor is switched off, a friction pad is applied to its circumference, bringing it to rest from an angular speed of $7.0 \text{ rad s}^{-1}$ in exactly $3$ revolutions. Determine the magnitude of the braking force applied by the friction pad.

[4]

Question 4

EasyPaper 2 · calculator4 marks

(a)

A flywheel in an energy storage system is accelerated uniformly from an angular velocity of $50\text{ rad s}^{-1}$ to $350\text{ rad s}^{-1}$ in a time of $25\text{ s}$ .

Calculate the angular acceleration of the flywheel.

[2]

(b)

Calculate the angular displacement of the flywheel during this $25\text{ s}$ interval.

[2]

Question 5

MediumPaper 2 · calculator4 marks

(a) A solid cylinder of mass $m = 2.5\text{ kg}$ and radius $r = 0.080\text{ m}$ is given an initial horizontal speed of $v = 4.0\text{ m s}^{-1}$ at the base of an inclined plane. The cylinder rolls without slipping up the incline. The moment of inertia of a solid cylinder about its central axis is $I = \frac{1}{2}mr^2$ .

Determine the maximum vertical height, $h$ , that the cylinder reaches up the incline.

Question 6

EasyPaper 2 · calculator2 marks

An electric motor drives a large industrial fan at a constant angular velocity of $120\text{ rad s}^{-1}$ . The motor supplies a useful power of $4.2\text{ kW}$ to the fan.

Calculate the magnitude of the torque exerted by the motor on the fan.

Question 7

MediumPaper 2 · calculator10 marks

(a)

A figure skater is spinning on a horizontal ice surface. There is a small frictional torque exerted by the ice on the skates.

(a) State and explain the effect of this frictional torque on the skater's angular momentum.

[2]

(b)

(b) While spinning, the skater pulls their arms in towards their body. Ignoring the effects of friction, explain why the total angular momentum of the skater is conserved during this action.

[2]

(c)

[3]

(d)

(d) Explain what happens to the skater's rotational kinetic energy when they pull their arms in.

[3]

Question 8

MediumPaper 2 · calculator4 marks

(a)

(a) A laboratory centrifuge starts from rest and uniformly increases its angular speed to $450 \text{ rad s}^{-1}$ in $15 \text{ s}$ . Calculate the angular acceleration of the centrifuge.

[2]

(b)

(b) Calculate the total angular displacement of the centrifuge during this $15 \text{ s}$ interval.

[2]

Question 9

MediumPaper 2 · calculator2 marks

(a) A large wind turbine generates electrical power at a rate of $1.5 \text{ MW}$ when its blades are rotating at $120 \text{ revolutions per minute (rpm)}$ . Calculate the magnitude of the torque exerted by the wind on the turbine shaft.

Question 10

MediumPaper 2 · calculator5 marks

(a)

A potter's wheel, designed with most of its mass concentrated at the rim, rotates around a central axis. Its angular speed is increased uniformly from $20 \text{ rad s}^{-1}$ to $80 \text{ rad s}^{-1}$ over a period of $4.0 \text{ s}$ . The wheel has a mass of $8.0 \text{ kg}$ and a radius of $30 \text{ cm}$ .

Calculate the work done by the motor's torque acting on the wheel.

[3]

(b)

Calculate the average power supplied to the wheel by the motor during this time.

[2]

Question 11

MediumPaper 2 · calculator4 marks

A horizontal playground carousel, initially rotating freely about a vertical axis through its centre, has a uniform rotational frequency of $0.50\text{ revolutions per second}$ . A child of mass $25\text{ kg}$ is standing at a distance of $1.5\text{ m}$ from the centre of the carousel. The child then walks towards the centre, stopping at a distance of $0.50\text{ m}$ from the centre. The rotational frequency of the carousel and child system increases to $0.65\text{ revolutions per second}$ .

Calculate the moment of inertia of the carousel.

Question 12

MediumPaper 2 · calculator5 marks

(a)

A large industrial flywheel, initially at rest, is subjected to a constant torque of $150 \text{ Nm}$ . The flywheel has a moment of inertia of $800 \text{ kg m}^2$ about its central axis.

(a) Calculate the angular acceleration produced.

[2]

(b)

(b) Calculate the linear speed of a point on the rim of the flywheel after $45 \text{ s}$ . The radius of the flywheel is $1.2 \text{ m}$ .

[3]

Question 13

MediumPaper 1A · calculator1 mark

A flywheel of moment of inertia $I$ is accelerated from rest by a constant net torque. The resulting angular acceleration $\alpha$ is constant.

What is the rotational kinetic energy of the flywheel after it has completed two full rotations?

A. $2\pi I\alpha$

B. $4\pi I\alpha$

C. $8\pi I\alpha$

D. $2I\alpha$

Question 14

MediumPaper 1A · calculator1 mark

A ceiling fan, initially at rest, accelerates uniformly for $10.0\text{ s}$ . The final angular velocity of the fan blades is $12\pi \text{ rad s}^{-1}$ .

How many revolutions did the fan blades complete during this time?

A. $15$

B. $30$

C. $60$

D. $120$

Question 15

MediumPaper 1A · calculator1 mark

A solid uniform cylinder of mass $M$ and radius $R$ rolls without slipping on a horizontal surface. The linear speed of its centre of mass is $v$ . The moment of inertia of the cylinder about its central axis is $I = \frac{1}{2}MR^2$ .

What is the ratio $\frac{\text{rotational kinetic energy}}{\text{total kinetic energy}}$ ?

A. $\frac{1}{4}$

B. $\frac{1}{3}$

C. $\frac{1}{2}$

D. $\frac{2}{3}$

Question 16

MediumPaper 1A · calculator1 mark

Two celestial bodies, a planet and a moon, are observed to have the same rotational kinetic energy about their respective axes. The planet has a moment of inertia $I_P$ and the moon has a moment of inertia $I_M$ .

What is the ratio $\frac{\text{angular momentum of the planet}}{\text{angular momentum of the moon}}$ ?

A. $\sqrt{\frac{I_P}{I_M}}$

B. $\sqrt{\frac{I_M}{I_P}}$

C. $\frac{I_P}{I_M}$

D. $\frac{I_M}{I_P}$

Question 17

MediumPaper 1A · calculator1 mark

A solid sphere of mass $M$ and radius $R$ is released from rest at the top of a ramp of vertical height $H$ . The sphere rolls without slipping.

The moment of inertia of a solid sphere about its center is $I = \frac{2}{5}MR^2$ .

What is the speed of the sphere when it reaches the bottom of the ramp?

A. $\sqrt{\frac{10}{7}gH}$

B. $\sqrt{2gH}$

C. $\sqrt{\frac{6}{5}gH}$

D. $\sqrt{\frac{4}{3}gH}$

Question 18

MediumPaper 1A · calculator1 mark

A laboratory experiment investigates the rotational motion of a uniform disk. The graph shows how the angular acceleration $\alpha$ of the disk varies with the net torque $\tau$ applied to it.

Graph of angular acceleration alpha in rad s^-2 versus torque tau in Nm. It's a straight line passing through (0,0) and (10, 4).

What is the moment of inertia of the disk?

A. $2.5 \text{ kg m}^2$

B. $0.40 \text{ kg m}^2$

C. $10 \text{ kg m}^2$

D. $40 \text{ kg m}^2$

Question 19

MediumPaper 2 · calculator3 marks

A horizontal circular platform rotates freely about a vertical axis through its centre with an angular velocity of $5.0\text{ rad s}^{-1}$ . A lump of clay of mass $50\text{ g}$ is dropped onto the platform and sticks to it at a distance of $15\text{ cm}$ from the axis of rotation. The angular velocity of the platform decreases to $4.0\text{ rad s}^{-1}$ .

Determine the moment of inertia of the platform.

Question 20

MediumPaper 2 · calculator5 marks

(a)

A uniform solid cylindrical flywheel rotates around an axis through its centre. The angular velocity of the flywheel is increased from $10.0\text{ rad s}^{-1}$ to $50.0\text{ rad s}^{-1}$ in $6.00\text{ s}$ . The mass of the flywheel is $30.0\text{ kg}$ and its radius is $0.500\text{ m}$ .

(a) Calculate the work done by the torque acting on the flywheel.

[3]

(b)

(b) Calculate the average power applied to the flywheel during this time.

[2]

5 more Rigid Body Mechanics questions in the app

Every answer is marked mark by mark, IB-style, and the AI tutor helps when you are stuck.

Where marks are lost

Stopping one step short of the conclusion. Two numbers and no sentence is two marks out of three.
Answering a procedure question with a platitude.
Losing precision in Paper 1B. Uniquely to this paper, quoting the right number badly loses marks.

Rigid Body Mechanics: notes and practice questions

How it is examined

Guiding questions

Linking questions