AP Physics 1 Quiz: Angular Momentum And Angular Impulse

What this quiz covers

This quiz focuses on Angular Momentum And Angular Impulse, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $8.0\,\text{kg·m}^2/\text{s}$
2. $2.0\,\text{kg·m}^2/\text{s}$ (correct answer)
3. $4.0\,\text{kg·m}^2/\text{s}$
4. $0.50\,\text{kg·m}^2/\text{s}$

Explanation: This question requires calculating angular impulse from constant torque and time duration. Angular impulse $J = \tau \Delta t$, where $\tau$ is the net torque and $\Delta t$ is the time interval. Substituting the given values: $J = (4.0 \, \text{N·m})(0.50 \, \text{s}) = 2.0 \, \text{N·m·s} = 2.0 \, \text{kg·m}^2/\text{s}$. The angular impulse represents the total angular effect of the torque over the time period. Choice A (8.0) incorrectly multiplies 4.0 by 2 instead of 0.50, suggesting a calculation error or misreading of the time value. To find angular impulse, always multiply the constant torque by the time duration.

Question 2

1. $-6.0\,\text{kg·m}^2/\text{s}$ (correct answer)
2. $-1.0\,\text{kg·m}^2/\text{s}$
3. $-60\,\text{kg·m}^2/\text{s}$
4. $6.0\,\text{kg·m}^2/\text{s}$

Explanation: This problem tests understanding of negative torque effects on angular momentum. The angular impulse J = τΔt = (-1.0 N·m)(6.0 s) = -6.0 kg·m²/s. Since angular impulse equals change in angular momentum, ΔL = -6.0 kg·m²/s. The negative value indicates the angular momentum decreases by this amount. Choice C (-60) incorrectly multiplies by an extra factor of 10, suggesting a decimal place error. When calculating change in angular momentum, multiply torque by time and preserve the sign to indicate direction.

Question 3

1. $0.50 \text{N·m}$ (correct answer)
2. $0.32 \text{N·m}$
3. $1.2 \text{N·m}$
4. $0.40 \text{N·m·s}$

Explanation: This question tests determining torque from angular momentum change and time. The positive change indicates torque direction aligns with increasing L, where $τ = ΔL / Δt$. Qualitatively, torque accelerates rotation, and its magnitude is the ratio of change to time. The constant nature simplifies to division. The distractor 0.40 N·m·s may confuse impulse with torque, a misconception of using ΔL directly as τ. Always solve for unknowns using $ΔL = τΔt$, ensuring proper algebraic isolation.

Question 4

1. $0.10 \text{kg·m}^2/\text{s}$
2. $30 \text{kg·m}^2/\text{s}$
3. $3.0 \text{kg·m}^2/\text{s}$
4. $0.30 \text{kg·m}^2/\text{s}$ (correct answer)

Explanation: This question evaluates angular impulse delivered to a flywheel. Angular impulse is $τ Δt$ for constant torque, matching the change in angular momentum. Qualitatively, it quantifies the rotational 'kick' from the torque over a short time. The flywheel receives this impulse directly. Choice C ($3.0 \text{kg·m}^2/\text{s}$) may be chosen by using torque without time, showing a misconception that impulse equals torque, not its time integral. Generally, reinforce understanding by comparing to linear impulse problems, noting the parallel structures in calculations.

Question 5

1. $36\,\text{N·m}$
2. $9.0\,\text{N·m}$
3. $4.0\,\text{N·m}$ (correct answer)
4. $12\,\text{N·m}$

Explanation: This problem requires finding torque from given change in angular momentum and time. Using the angular impulse-momentum theorem: ΔL = τΔt, we can solve for torque: τ = ΔL/Δt = (12 kg·m²/s)/(3.0 s) = 4.0 N·m. The torque represents the rate of change of angular momentum. A larger torque would produce the same momentum change in less time. Choice A (36) incorrectly multiplies instead of dividing, showing confusion about rearranging the impulse equation. To find torque from momentum change and time, divide the momentum change by the time duration.

Question 6

1. $6.0\ \text{kg·m}^2/\text{s}$ (correct answer)
2. $0.38\ \text{kg·m}^2/\text{s}$
3. $1.5\ \text{kg·m}^2/\text{s}$
4. $4.0\ \text{kg·m}^2/\text{s}$

Explanation: This question examines the direct link between net torque, time, and magnitude of change in angular momentum. Net torque over time delivers angular impulse, which equals the absolute change in angular momentum. Qualitatively, longer torque application or stronger torque leads to greater momentum change. No initial conditions are needed since only the change is requested. The distractor 1.5 kg·m²/s may come from using torque alone, a misconception of equating torque to momentum change without time. Strategically, always multiply constant torque by time to find ΔL, mirroring linear dynamics.

Question 7

1. $0.50\ \text{kg·m}^2/\text{s}$ (correct answer)
2. $12.5\ \text{kg·m}^2/\text{s}$
3. $2.5\ \text{kg·m}^2/\text{s}$
4. $0.20\ \text{kg·m}^2/\text{s}$

Explanation: This question explores the magnitude of angular momentum change due to net torque over time. Net torque produces impulse, equaling ΔL in magnitude. Longer time or higher torque amplifies the change qualitatively. Only the product matters for magnitude. The distractor 2.5 kg·m²/s might use torque value alone, a misconception of omitting time in impulse. A key strategy is to identify if the question seeks change (τΔt) versus rate (τ), applying the formula accordingly.

Question 8

1. $6.0\,\text{kg·m}^2/\text{s}$ (correct answer)
2. $1.5\,\text{kg·m}^2/\text{s}$
3. $4.0\,\text{kg·m}^2/\text{s}$
4. $0\,\text{kg·m}^2/\text{s}$

Explanation: This question tests calculating final angular momentum when starting from rest with constant torque. The angular impulse J = τΔt = (1.5 N·m)(4.0 s) = 6.0 kg·m²/s. Since the rotor starts from rest (Li = 0), the final angular momentum equals the angular impulse: Lf = Li + ΔL = 0 + 6.0 = 6.0 kg·m²/s. Starting from rest means all the angular impulse becomes the final angular momentum. Choice B (1.5) incorrectly uses only the torque value without multiplying by time, confusing torque with angular momentum. Remember that angular momentum change equals torque multiplied by time, not just torque alone.

Question 9

1. $2.0 \text{N·m·s}$ (correct answer)
2. $8.0 \text{N·m·s}$
3. $4.0 \text{N·m}$
4. $0.50 \text{N·m·s}$

Explanation: This question evaluates understanding of angular impulse delivered by a constant torque over time. Angular impulse is the product of constant torque and the time interval, representing the total 'push' in the rotational sense. It quantifies how much the angular momentum changes, but here the question directly asks for the impulse itself. The low-friction axle implies negligible other torques, so the given torque is net. A distractor like $4.0 \text{N·m}$ could arise from mistaking torque for impulse, a misconception of overlooking the multiplication by time. Remember as a strategy that impulse always involves integrating force or torque over time, ensuring units include seconds.

Question 10

1. $2.0 \text{N·m·s}$ (correct answer)
2. $0.031 \text{N·m·s}$
3. $8.0 \text{N·m}$
4. $0.25 \text{kg·m}^2/\text{s}$

Explanation: This question evaluates computing angular impulse from constant torque and duration. Angular impulse is $τ Δt$ for constant torque, measuring total rotational effect. It relates qualitatively to how much spin is imparted, with units $\text{N·m·s}$. The magnitude ignores direction here. A distractor like 8.0 $\text{N·m}$ might use time alone, a misconception of swapping torque and time in the product. Strategically, recall impulse as area under torque-time graph; for constant, it's simple multiplication.

Question 11

1. $12\ \text{N·m}$
2. $3.0\ \text{N·m}$ (correct answer)
3. $8.0\ \text{N·m}$
4. $4.0\ \text{N·m}$

Explanation: This question probes finding torque from change in angular momentum and time. The relationship ΔL = τ Δt allows solving for τ as ΔL / Δt when torque is constant. Qualitatively, torque drives the rate of angular momentum change, so averaging over time gives the constant value. The disk's increase in L directly informs the torque magnitude. Distractor A (12 N·m) might occur from multiplying instead of dividing ΔL by time, indicating a reversal misconception in the formula application. To generalize, always isolate the unknown variable algebraically before plugging in numbers to avoid arithmetic errors.

Question 12

1. $8.0\ \text{kg·m}^2/\text{s}$
2. $2.0\ \text{kg·m}^2/\text{s}$ (correct answer)
3. $4.0\ \text{kg·m}^2/\text{s}$
4. $0.50\ \text{kg·m}^2/\text{s}$

Explanation: This question evaluates knowledge of angular impulse in the context of rotational motion. Angular impulse results from a torque applied over a time interval and is calculated as τ Δt for constant torque. It represents the total change in angular momentum imparted to the system, similar to how force over time changes linear momentum. In this case, the motor delivers this impulse directly to the wheel. A common distractor like choice C (4.0 kg·m²/s) could arise from forgetting to multiply by time and just using the torque value, indicating a misconception of impulse as instantaneous rather than time-integrated. To approach such problems effectively, always verify units: angular impulse has units of kg·m²/s, matching angular momentum.

Question 13

1. $2.1\,\text{kg·m}^2/\text{s}$
2. $3.0\,\text{kg·m}^2/\text{s}$ (correct answer)
3. $2.5\,\text{kg·m}^2/\text{s}$
4. $1.2\,\text{kg·m}^2/\text{s}$

Explanation: This question requires calculating change in angular momentum from torque and time. Using the angular impulse-momentum theorem: $\Delta L = \tau \Delta t = (2.5 \, \text{N·m})(1.2 \, \text{s}) = 3.0 \, \text{kg·m}^2/\text{s}$. The change represents how much the angular momentum increases due to the applied torque. The calculation is straightforward multiplication of the two given values. Choice A (2.1) might result from calculation error or misreading the values, while C (2.5) incorrectly uses just the torque value. Always multiply torque by time to find the change in angular momentum.

Question 14

1. $3.2\,\text{s}$
2. $0.50\,\text{s}$
3. $2.0\,\text{s}$ (correct answer)
4. $1.2\,\text{s}$

Explanation: This problem involves finding time duration from torque and angular momentum change. From ΔL = τΔt, we solve for time: Δt = ΔL/τ = (0.80 kg·m²/s)/(0.40 N·m) = 2.0 s. The time represents how long the torque must act to produce the given momentum change. Smaller torque requires more time for the same momentum change. Choice B (0.50) incorrectly multiplies the values instead of dividing, showing confusion about rearranging the impulse equation. To find time from momentum change and torque, divide the momentum change by the torque.

Question 15

1. $0.33\ \text{s}$
2. $1.2\ \text{s}$
3. $3.0\ \text{s}$ (correct answer)
4. $2.4\ \text{s}$

Explanation: This scenario tests calculating time from change in angular momentum and torque. Rearranging ΔL = τ Δt gives Δt = ΔL / τ for constant torque. This reflects the duration needed for torque to effect the momentum change. The wheel's constant torque determines this time. Choice D (2.4 s) could result from dividing incorrectly, like 1.8 / 0.75, indicating a numerical misconception in division. A transferable approach is to check reasonability: larger ΔL or smaller τ should yield longer times, aiding error detection.

Question 16

1. $0.16\,\text{N·m}$
2. $4.0\,\text{N·m}$ (correct answer)
3. $0.80\,\text{N·m}$
4. $1.0\,\text{N·m}$

Explanation: This question involves finding torque from angular impulse and time duration. The angular impulse J = τΔt, so τ = J/Δt = (0.80 kg·m²/s)/(0.20 s) = 4.0 N·m. The torque must be sufficient to produce the given angular impulse in the specified time. Shorter time requires larger torque for the same impulse. Choice A (0.16) incorrectly multiplies the two given values instead of dividing, revealing confusion about the relationship between impulse, torque, and time. When given angular impulse and time, divide impulse by time to find the constant torque.

Question 17

1. $0.53 \text{ kg·m}^2/\text{s}$
2. $0.30 \text{ kg·m}^2/\text{s}$ (correct answer)
3. $1.15 \text{ kg·m}^2/\text{s}$
4. $0.40 \text{ kg·m}^2/\text{s}$

Explanation: This problem assesses computing change in angular momentum from torque and time. For constant torque, $\Delta L$ equals $\tau$ times $\Delta t$, embodying the angular impulse. This ties into how sustained torque accumulates change in rotational momentum over time. The wheel experiences this direct proportionality. Choice C ($1.15 \text{ kg·m}^2/\text{s}$) could be selected by adding torque and time instead of multiplying, revealing a misconception about the multiplicative nature of impulse. A key strategy is to memorize the rotational equivalents: force $\to$ torque, momentum $\to$ angular momentum, impulse $\to$ angular impulse.

Question 18

1. $6.0 \, \text{kg·m}^2/\text{s}$
2. $8.0 \, \text{kg·m}^2/\text{s}$ (correct answer)
3. $7.5 \, \text{kg·m}^2/\text{s}$
4. $9.0 \, \text{kg·m}^2/\text{s}$

Explanation: This question tests applying positive torque to increase angular momentum. The angular impulse $J = \tau \Delta t = (+0.50 \, \text{N·m})(2.0 \, \text{s}) = +1.0 \, \text{kg·m}^2/\text{s}$. The final angular momentum is $L_f = L_i + \Delta L = 7.0 + 1.0 = 8.0 \, \text{kg·m}^2/\text{s}$. The positive torque adds to the existing angular momentum in the same direction. Choice A (6.0) incorrectly subtracts instead of adding, treating the positive torque as negative. When torque and initial angular momentum have the same sign, add the angular impulse to find final angular momentum.

Question 19

1. $0.63 \, \text{kg·m}^2/\text{s}$
2. $6.5 \, \text{kg·m}^2/\text{s}$
3. $10 \, \text{kg·m}^2/\text{s}$ (correct answer)
4. $2.5 \, \text{kg·m}^2/\text{s}$

Explanation: This question involves determining change in angular momentum for a spinning platform. The net torque over time produces angular impulse, equaling $ΔL$. Qualitatively, this shows how external torques alter a system's rotational state. The constant net torque here results in a straightforward calculation. Distractor B ($6.5 \, \text{kg·m}^2/\text{s}$) might arise from using 2.5 * 2.6 or a miscalculation, pointing to an arithmetic misconception rather than conceptual error. For wider application, use the formula $ΔL = τ Δt$ as a checkpoint in more complex rotational problems involving moments of inertia.

Question 20

1. $1.7 \text{kg·m}^2/\text{s}$
2. $0.20 \text{kg·m}^2/\text{s}$
3. $0.30 \text{kg·m}^2/\text{s}$ (correct answer)
4. $7.5 \text{kg·m}^2/\text{s}$

Explanation: This question focuses on calculating the change in angular momentum from a given torque and time. Angular momentum changes when a net torque is applied, with the magnitude of change given by $\Delta L = \tau \Delta t$ for constant torque. This qualitative link mirrors the linear case where impulse equals change in momentum. Here, the fan blade's axle torque causes the specified change. Distractor D ($7.5 \text{kg·m}^2/\text{s}$) could result from multiplying torque by time incorrectly, like using 1.5 * 5 instead of 0.20 s, showing a misconception in reading the time value accurately. For transferable skills, practice dimensional analysis to ensure calculations yield the correct units for angular momentum.