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American System Physics

A Physics Toolkit

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Representing Motion

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Accelerated Motion

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Forces in One Dimension

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Displacement and Force in Two Dimensions

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Motion in Two Dimensions

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Gravitation

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Rotational Motion

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Momentum and Its Conservation

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Energy and Its Conservation

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Thermal Energy

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States of Matter

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Vibrations and Waves

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Sound

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Fundamentals of Light

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Reflection and Refraction

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Interference and Diffraction

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Electrostatics

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Electric Current and Circuits

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Magnetic Fields

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Electromagnetic Induction and Electromagnetism

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Quantum Theory and the Atom

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Solid-State Electronics

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Quiz

8.2 Rotational Dynamics: Torque and Moment of Inertia – Quiz

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Rotational Dynamics American Physics quiz: free practice for American System Physics. Work through this Rotational Dynamics American Physics quiz and get instant feedback on every answer. If you get stuck, review the 8.2 Rotational Dynamics: Torque and Moment of Inertia — Notes lesson. More practice: American System Physics — all units. Syllabus: OpenStax free science textbooks.

  • Questions count: 50
  • Passing grade: A-
  • Time limit:
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1.
A mechanic pulls on a wrench with a force of 60 N as shown. Using the diagram, what is the magnitude of the torque produced about the bolt?
Dr Dabour Hub Academy - figure 1
30.0 N·m
15.0 N·m
120 N·m
60.0 N·m
2.
Two tangential forces act on the pulley shown. What is the net torque about the axle? (counterclockwise positive)
Dr Dabour Hub Academy - figure 2
10.5 N·m (counterclockwise)
−1.5 N·m (clockwise)
−3.0 N·m (clockwise)
+1.5 N·m (counterclockwise)
3.
The three objects in the diagram are released together and roll down their identical ramps. Which reaches the bottom first, and why?
Dr Dabour Hub Academy - figure 3
The hoop, because its mass is at the rim
The solid sphere, because it has the smallest I/(mr²), so least of its energy goes into rotation
All arrive together because they have the same mass
The solid disc, because it has the largest moment of inertia
4.
The diagram shows four 20 N forces that could be applied to a door (top view). Which force produces the largest torque about the hinge?
Dr Dabour Hub Academy - figure 4
B
C
A
D
5.
For the force shown in the diagram, what is the lever arm (moment arm) about the pivot?
Dr Dabour Hub Academy - figure 5
0.32 m
0.38 m
0.50 m
0.78 m
6.
The graph shows angular acceleration against net torque for wheels A and B. What is the moment of inertia of wheel B?
Dr Dabour Hub Academy - figure 6
1.25 kg·m²
0.25 kg·m²
2.5 kg·m²
0.80 kg·m²
7.
A student pulls with a constant 20 N force on a lever at different angles θ and measures the torque with a sensor (graph). What distance from the pivot was the force applied?
Dr Dabour Hub Academy - figure 7
7.0 m
0.70 m
0.35 m
0.18 m
8.
The diagram shows a 0.5 kg mass and a 3.0 kg mass on a light rod that rotates about the axis shown. What is the moment of inertia of the system about this axis?
Dr Dabour Hub Academy - figure 8
1.90 kg·m²
1.10 kg·m²
2.24 kg·m²
1.82 kg·m²
9.
A 40 kg child and a 50 kg adult sit on the seesaw in the diagram, which is balanced. Using the principle of moments, what is the distance d?
Dr Dabour Hub Academy - figure 9
1.88 m
1.20 m
1.50 m
0.533 m
10.
A student tests four ways of turning a lever and records the force, distance from the pivot and angle (table). Which trial gives the largest torque?
Trial Q
Trial P
Trial R
Trial S
11.
Using the table, how does the moment of inertia of a 3.0 kg, 1.2 m rod about one end compare with that about its centre?
2 times larger
3 times larger
12 times larger
4 times larger
12.
Students time a hoop, a solid disc and a solid sphere (same mass and radius) rolling down the same ramp (table). Which conclusion is supported?
Heavier objects roll faster
Objects with a smaller moment of inertia for their mass and radius roll down faster
The shape of an object does not affect its rolling time
Objects with more mass at the rim roll faster
13.
Using the table, which flywheel stores the most rotational kinetic energy?
Flywheel C
Flywheel A
Flywheel B
They all store the same energy
14.
A student balances a metre rule pivoted at its centre by moving weight W2 (table). Which conclusion is best supported?
W2 is directly proportional to d2
W2 + d2 is constant
The rule's own weight produces the largest moment
W2 × d2 is constant (equal to W1 × d1) apart from one anomalous row, confirming the principle of moments
15.
A wheel nut must be tightened to 110 N·m. A mechanic can push with at most 300 N at right angles to the spanner. Using the table, which spanners can do the job?
Only the 0.25 m spanner
All three spanners
Only the 0.60 m spanner
The 0.40 m and 0.60 m spanners
16.
Two equal masses are clamped on a light rod at equal distances d from the axis, and the same torque is applied each time (table). What does the pattern show?
α is proportional to d
The position of the masses has no effect on α
Moving mass farther from the axis increases I, so α falls (roughly as 1/d²)
Moving the masses outward decreases I
17.
A student applies different torques to a flywheel and measures its angular acceleration (table). What is the best estimate of the flywheel's moment of inertia?
20 kg·m²
0.49 kg·m²
0.049 kg·m²
0.025 kg·m²
18.
A tangential force of 2.0 N acts on the rim of a solid disc (mass 4.0 kg, radius 0.2 m) free to rotate about an axis through its centre, perpendicular to its face. What is its angular acceleration?
5.00 rad/s²
25.0 rad/s²
2.50 rad/s²
0.0320 rad/s²
19.
A student investigates how the angular acceleration of a wheel depends on the torque applied by a falling mass. Which variable must be kept constant?
The wheel's moment of inertia (same wheel, no added masses)
The size of the falling mass
The angular acceleration
The torque
20.
Newton's second law has a rotational version. Which pairing of linear quantity and its role in τ = Iα is correct?
Mass m – corresponds to angular acceleration α
Force F – corresponds to torque τ
Acceleration a – corresponds to moment of inertia I
Force F – corresponds to angular velocity ω
21.
An engineer adjusts the torque on a wheel or its moment of inertia. Which pairing of change and effect on angular acceleration is correct?
Double I, same torque – α doubles
Halve the torque, same I – α unchanged
Double the torque, same I – α doubles
Double both torque and I – α quadruples
22.
A solid disc of mass 4.0 kg and radius 0.25 m spins at 20 rad/s about its central axis. What is its rotational kinetic energy?
25 J
50 J
1.25 J
10 J
23.
Why is it easier to open a door by pushing at the handle rather than near the hinges?
The door is lighter at the handle end
The force is larger at the handle
Friction is smaller at the handle
The larger distance from the hinge gives a larger torque for the same force
24.
In a principle-of-moments experiment with a metre rule, why is the rule pivoted at its centre (50 cm mark)?
So the rule is as heavy as possible
So the rule's own weight acts through the pivot and has no moment
Because the centre is where the rule is strongest
To make the lever arms as large as possible
25.
What is the moment of inertia of a hoop of mass 2.0 kg and radius 0.1 m about an axis through its centre, perpendicular to its plane?
0.0100 kg·m²
8.00 × 10⁻³ kg·m²
0.0200 kg·m²
1.67 × 10⁻³ kg·m²
26.
A data book lists moments of inertia for common shapes. Which pairing of object and moment of inertia about its centre is correct?
hoop – ½mr²
solid sphere – (2/5)mr²
solid disc – mr²
thin rod – (1/3)ml²
27.
A student lists ways to get more turning effect from a force. Which pairing of method and reason it increases torque is correct?
Push along the door towards the hinge – sin θ = 1
Push more gently – τ ∝ 1/F
Push farther from the hinge – τ ∝ r
Push at the hinge – lever arm is largest
28.
On a seesaw, a 300 N child sits 2.0 m left of the pivot and a 200 N child sits 1.0 m left of the pivot. Where must a 400 N adult sit on the right to balance them?
1.25 m right of the pivot
1.5 m right of the pivot
4.0 m right of the pivot
2.0 m right of the pivot
29.
Everyday situations illustrate rotational ideas. Which pairing of situation and physics idea is correct?
Long spanner – decreases the lever arm
Door handle far from the hinge – reduces the torque
Two hands on a steering wheel – produce a resultant force
Tightrope walker's long pole – increases moment of inertia
30.
The same torque is applied to a thin rod, first about an axis through its centre and then about an axis through one end. How do the angular accelerations compare?
α about the end is 4 times α about the centre
They are equal because the rod is the same
α about the centre is 4 times α about the end
α about the centre is 3 times α about the end
31.
A wheel with moment of inertia 0.60 kg·m² must go from rest to 30 rad/s in 5.0 s. What net torque is needed?
18 N·m
3.6 N·m
0.72 N·m
6.0 N·m
32.
Newton's second law for rotation states that net torque = moment of inertia × _____.
angular velocity
linear acceleration
angular acceleration
angular displacement
33.
The perpendicular distance from the pivot to the line of action of a force is called the _____.
lever arm
line of action
radius of gyration
couple
34.
Two equal, opposite, parallel forces whose lines of action do not coincide form a _____.
lever
moment arm
pivot
couple
35.
The rotational kinetic energy of an object is equal to _____.
Iω²
½Iω
½mω²
½Iω²
36.
The moment of inertia of a solid sphere about an axis through its centre is _____.
(2/5)mr²
½mr²
mr²
(1/12)mr²
37.
For a point mass m at distance r from an axis, the moment of inertia is I = _____.
mr
mr²
½mr²
m/r²
38.
A force whose line of action passes through the pivot produces zero torque. True or false?
True
False
False, because it produces maximum torque
True only when the force is very large
39.
Torque is measured in N·m, and the lever arm is the perpendicular distance from the pivot to the line of action of the force. True or false?
False
False, because torque is measured in N/m
True
True only when the force is perpendicular to the lever
40.
A spinning skater speeds up when pulling their arms in because their moment of inertia decreases. True or false?
True
False
False, because their moment of inertia increases
True only when they push on the ice
41.
If the net torque on a wheel is multiplied by 3 while its moment of inertia is unchanged, its angular acceleration is multiplied by 9. True or false?
True
True only when the wheel starts from rest
False, because α = τ/I, so α is multiplied by 3
False, because α is unchanged
42.
Pushing a door right next to its hinge produces the largest torque for a given force. True or false?
True
True only when the door is heavy
False, because close to the hinge the lever arm is tiny, so the torque is very small
False, because torque does not depend on where the force acts
43.
In a flywheel experiment, ignoring friction at the axle makes the calculated moment of inertia (applied torque ÷ α) larger than the true value. True or false?
False
False, because it makes the value smaller
True
True only when the flywheel is light
44.
An object's moment of inertia depends only on its mass, not on how the mass is distributed. True or false?
False, because I depends on how far the mass is from the axis; the same mass farther out gives a larger I
True
True only when the object is a sphere
False, because it depends only on its shape, not its mass
45.
A hoop and a solid disc of the same mass and radius have the same moment of inertia about their central axes. True or false?
True
True only when they rotate at the same speed
False, because the hoop's mass is all at the rim, so I = mr², twice the disc's ½mr²
False, because the disc has the larger moment of inertia
46.
A thin rod has the same moment of inertia about its end as about its centre. True or false?
True
False, because about its end I = (1/3)ml², four times the (1/12)ml² about its centre
True only when the rod is uniform
False, because it is smaller about its end
47.
When rolling from rest down the same slope, a solid sphere reaches the bottom before a hoop of the same mass and radius. True or false?
False
False, because the hoop always wins
True only when the slope is frictionless
True
48.
If the moment of inertia of a wheel is doubled while the net torque stays the same, its angular acceleration is halved. True or false?
False
True
False, because α is doubled
True only when the wheel starts from rest
49.
The torque of a couple equals the size of one of the forces multiplied by the perpendicular distance between their lines of action. True or false?
False
False, because it equals the sum of the two forces times the distance from the centre
True only when the forces act on a steering wheel
True
50.
By convention, counterclockwise torques are taken as positive and clockwise torques as negative. True or false?
False
True
False, because clockwise torques are positive
True only when the pivot is on the left
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Part of Rotational Motion — see every lesson and quiz in this unit.
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