Master Rotational Motion with AP Physics 1 review games.
This unit covers torque, angular velocity, rotational inertia and angular momentum — essential concepts for AP Physics 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers torque, angular velocity, rotational inertia and angular momentum — essential concepts for AP Physics 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Torque
Torque is the rotational equivalent of force, defined as τ = rF sinθ, where r is the lever arm distance, F is the applied force, and θ is the angle between them. Students must be able to calculate net torque, determine rotational direction (clockwise vs. counterclockwise), and apply Newton's second law in rotational form: τ_net = Iα. Torque problems frequently involve static equilibrium, where the sum of all torques equals zero.
Key Points
- τ = rF sinθ; maximum torque occurs when force is perpendicular to the lever arm (θ = 90°)
- Torque is a vector: counterclockwise is conventionally positive, clockwise is negative
- For rotational equilibrium: Στ = 0 and ΣF = 0 must both hold
- The lever arm is the perpendicular distance from the pivot to the line of action of the force
A uniform 4 m beam weighing 200 N is supported at its left end by a hinge and by a cable attached 3 m from the left end. A 100 N weight hangs from the right end. Find the tension in the cable.
Set the pivot at the hinge to eliminate the unknown hinge force from the torque equation. The beam's weight (200 N) acts at the center (2 m from hinge), and the hanging weight (100 N) acts at 4 m. Setting Στ = 0: T(3) − 200(2) − 100(4) = 0, giving T = 800/3 ≈ 267 N. Always place the pivot at an unknown force to reduce variables.
2 Angular Velocity
Angular velocity (ω) measures how fast an object rotates, in radians per second, and is the rotational analog of linear velocity. Students must know the kinematic equations for constant angular acceleration (mirroring linear kinematics) and the relationship between linear and angular quantities: v = rω and a_t = rα. The AP exam tests both the conceptual understanding of these relationships and their application in two-step problems.
Key Points
- ω = Δθ/Δt (rad/s); α = Δω/Δt (rad/s²)
- Rotational kinematics: ω = ω₀ + αt, θ = ω₀t + ½αt², ω² = ω₀² + 2αθ
- Linear speed at radius r: v = rω — points farther from the axis move faster
- Period and angular velocity are related by: ω = 2π/T
A wheel starts from rest and reaches 120 rpm in 4 seconds with constant angular acceleration. How many revolutions does it complete in that time?
Convert 120 rpm to rad/s: ω = 120 × (2π/60) = 4π rad/s. Find α = Δω/Δt = 4π/4 = π rad/s². Use θ = ω₀t + ½αt² = 0 + ½(π)(16) = 8π rad. Convert to revolutions: 8π / 2π = 4 revolutions. Unit conversion between rpm and rad/s is a common exam trap.
3 Rotational Inertia
Rotational inertia (moment of inertia, I) is the rotational analog of mass and measures an object's resistance to changes in rotational motion. Its value depends on both the total mass and how that mass is distributed relative to the rotation axis — mass farther from the axis contributes more. On the AP exam, students are given standard formulas (e.g., I = ½MR² for a solid disk, I = MR² for a hoop) and must apply them in Newton's second law for rotation: τ_net = Iα.
Key Points
- I = Σmr²; the farther mass is from the axis, the greater the rotational inertia
- Common formulas given on the AP exam: solid disk I = ½MR², hoop I = MR², rod about center I = (1/12)ML²
- Greater I means harder to angularly accelerate for the same net torque
- When mass redistributes (e.g., arms pulled in on a spinning stool), I changes and angular momentum is conserved
A solid disk (mass 2 kg, radius 0.5 m) and a hoop (same mass and radius) are released from rest at the top of the same incline. Which reaches the bottom first?
The disk has I = ½MR² and the hoop has I = MR², so the hoop has greater rotational inertia relative to its mass. Using energy conservation, more energy goes into rotation for the hoop, leaving less for translational KE — so the disk has greater linear acceleration and reaches the bottom first. This is a classic AP exam reasoning question that tests conceptual understanding of how I affects motion.
4 Angular Momentum
Angular momentum (L = Iω) is the rotational analog of linear momentum and is conserved when no net external torque acts on a system. Students must be able to apply conservation of angular momentum to problems involving changing rotational inertia (e.g., a figure skater pulling arms in) and collisions involving rotating objects. The AP exam also tests the impulse-momentum theorem in rotational form: τ_net × Δt = ΔL.
Key Points
- L = Iω (kg·m²/s); direction follows the right-hand rule (not required for AP 1 but the sign convention is)
- Conservation of angular momentum: if Στ_ext = 0, then L_i = L_f, so I₁ω₁ = I₂ω₂
- Angular impulse: τ_net · Δt = ΔL (analogous to linear impulse-momentum theorem)
- A point mass moving in a straight line can have angular momentum about an off-path axis: L = mvr sinθ
A student sits on a frictionless rotating stool holding 2 kg masses at arm's length (r = 0.8 m) and spins at 2 rad/s. She pulls the masses to r = 0.2 m. The stool + student system has I_body = 3 kg·m². Find her new angular velocity.
Initial I_total = I_body + 2mr² = 3 + 2(2)(0.8²) = 3 + 2.56 = 5.56 kg·m². Final I_total = 3 + 2(2)(0.2²) = 3 + 0.16 = 3.16 kg·m². By conservation of angular momentum: ω_f = L_i/I_f = (5.56 × 2)/3.16 ≈ 3.52 rad/s. Since no external torque acts, angular momentum is conserved even though kinetic energy increases (the student does work pulling the masses inward).
Questions, answered.
What is Rotational Motion?
Rotational Motion is Unit 5 of AP Physics 1, covering torque, angular velocity, rotational inertia and angular momentum.
How to study for AP Physics 1 Unit 5?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 30+ review questions across 5 different game modes.