AP Physics 1 Quiz: Newtons Second Law In Rotational Form

What this quiz covers

This quiz focuses on Newtons Second Law In Rotational Form, 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. $\tau$ must decrease by a factor of $5$.
2. $\tau$ must increase by a factor of $5$. (correct answer)
3. $\tau$ is unchanged because torque depends only on force direction.
4. $\tau$ becomes proportional to angular velocity, so it increases over time.

Explanation: This problem applies Newton's second law in rotational form to find the required torque when inertia changes. The key equation is τ_net = I·α, which shows that to maintain constant angular acceleration when rotational inertia changes, the torque must change proportionally. If the flywheel's rotational inertia increases by a factor of 5 (from I to 5I) while keeping α constant, then τ_new = (5I)·α = 5(I·α) = 5τ. The torque must increase by a factor of 5 to maintain the same angular acceleration with five times the rotational inertia. Choice A incorrectly suggests decreasing the torque, which would actually reduce the angular acceleration. When solving for required torque, remember that τ and I must change by the same factor to keep α constant.

Question 2

1. $\alpha$ decreases because less inertia means less rotation.
2. $\alpha$ increases because $\alpha=\tau/I$. (correct answer)
3. $\alpha$ stays the same because torque sets angular acceleration directly.
4. $\alpha$ depends on angular velocity, so it cannot be determined.

Explanation: This question tests understanding of Newton's second law in rotational form when rotational inertia decreases. The fundamental relationship is τ_net = I·α, which rearranges to α = τ_net/I, showing that angular acceleration is inversely proportional to rotational inertia when torque is constant. When the cylinder is replaced with an object having smaller rotational inertia but the same net torque is applied, the angular acceleration must increase because we're dividing the same torque by a smaller inertia. Choice C incorrectly suggests that torque directly determines angular acceleration without considering inertia, missing the key role that I plays in rotational dynamics. When analyzing rotational motion, always consider both torque and rotational inertia to determine angular acceleration.

Question 3

1. $\alpha$ increases because a larger $I$ means more torque is “stored.”
2. $\alpha$ decreases because $\alpha=\tau/I$. (correct answer)
3. $\alpha$ is unchanged because torque depends only on force and lever arm.
4. $\alpha$ increases because $\tau$ is proportional to angular velocity.

Explanation: This question tests Newton's second law in rotational form. Newton's second law for rotation states that the net torque equals the rotational inertia times the angular acceleration: τ_net = I·α. When a constant net torque acts on a rotating object, the angular acceleration depends inversely on the rotational inertia—objects with larger I are harder to accelerate rotationally, just as objects with larger mass are harder to accelerate linearly. Since α = τ/I, if τ remains constant but I increases, then α must decrease proportionally. Choice A incorrectly suggests that torque can be "stored" in rotational inertia, which confuses the concepts. To solve problems like this, identify what quantities remain constant (here, τ) and apply the rotational form of Newton's second law algebraically.

Question 4

1. Wheel 2 has greater $\alpha$ because it has more mass.
2. Wheel 2 has smaller $\alpha$ because $\alpha=\tau/I$. (correct answer)
3. Both have the same $\alpha$ because they have the same net torque.
4. Both have the same $\alpha$ if they start with the same angular velocity.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, for the same torque, an object with greater rotational inertia will experience smaller angular acceleration due to increased resistance to rotational change. The relationship is inverse: α decreases as I increases. Thus, wheel 2 with greater I has smaller α than wheel 1 under the same τ. A common distractor is choice C, stating both have the same α because of the same net torque, but this overlooks inertia's role. When comparing accelerations in similar scenarios, always account for differences in I by using α = τ / I for each object.

Question 5

1. $\alpha$ becomes four times larger.
2. $\alpha$ becomes twice as large.
3. $\alpha$ is unchanged. (correct answer)
4. $\alpha$ becomes half as large.

Explanation: This question examines Newton's second law in rotational form when both torque and inertia change proportionally. The key relationship is τ_net = I·α, which gives us α = τ_net/I. If both the numerator (torque) and denominator (rotational inertia) are doubled, we get α_new = (2τ)/(2I) = τ/I = α. The angular acceleration remains unchanged because the ratio of torque to inertia stays the same. Choice A incorrectly suggests the acceleration quadruples, perhaps by mistakenly multiplying the two factors of 2. When both τ and I change by the same factor, their ratio (and thus α) remains constant—this is a key insight for analyzing rotational dynamics.

Question 6

1. It doubles.
2. It stays the same.
3. It becomes half as large. (correct answer)
4. It becomes zero because the bar resists rotation.

Explanation: This question applies Newton's second law in rotational form to analyze how angular acceleration changes with rotational inertia. The rotational form states τ_net = I·α, which means the net torque equals the product of rotational inertia and angular acceleration. When net torque is constant, angular acceleration is inversely proportional to rotational inertia: α = τ_net/I. If the rotational inertia doubles while torque remains constant, the angular acceleration becomes half as large because you're dividing the same torque by twice the inertia. Choice D incorrectly suggests the bar would stop rotating, but objects don't "resist" rotation—they simply require more torque to achieve the same angular acceleration when they have more rotational inertia. Remember that doubling I while keeping τ constant always halves α.

Question 7

1. $\alpha_1>\alpha_2$ because larger inertia means more torque effect.
2. $\alpha_1=\alpha_2$ because the torques are equal.
3. $\alpha_1<\alpha_2$ because $\alpha=\tau/I$. (correct answer)
4. Their angular accelerations depend only on their angular velocities.

Explanation: This question compares angular accelerations using Newton's second law in rotational form. The fundamental relationship τ_net = I·α rearranges to α = τ_net/I, showing that angular acceleration is inversely proportional to rotational inertia when torque is constant. Since both wheels experience the same net torque magnitude but wheel 1 has larger rotational inertia than wheel 2, we can write α₁ = τ/I₁ and α₂ = τ/I₂. Because I₁ > I₂ and the torques are equal, we must have α₁ < α₂—the wheel with larger inertia has smaller angular acceleration. Choice A incorrectly reverses this relationship, suggesting larger inertia leads to greater angular acceleration. To compare angular accelerations, always check which object has larger I: the one with larger I will have smaller α for the same torque.

Question 8

1. It doubles. (correct answer)
2. It halves.
3. It is unchanged because $\alpha$ depends on angular velocity.
4. It becomes zero because clockwise torque cancels clockwise acceleration.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, this relationship shows that angular acceleration is the result of net torque divided by rotational inertia, meaning torque drives the change in rotational motion. When rotational inertia is constant, increasing the net torque directly increases the angular acceleration in proportion. This is analogous to linear motion where doubling the force doubles the acceleration for a fixed mass. A common distractor is choice C, which wrongly suggests angular acceleration depends on angular velocity, but α is independent of current ω and depends only on τ_net and I. To solve these problems effectively, isolate the changing variable in τ_net = I α and determine its proportional impact on α.

Question 9

1. It doubles because $\tau$ is proportional to angular velocity.
2. It halves because faster rotation reduces torque.
3. It is unchanged because $\alpha$ depends on $\tau_{\text{net}}$ and $I$. (correct answer)
4. It becomes zero because constant torque cannot act at higher speed.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, this law indicates that angular acceleration depends solely on current net torque and rotational inertia, not on the existing angular velocity. Changing the angular velocity without altering τ_net or I leaves α unaffected. The acceleration remains constant as long as τ_net and I are fixed, regardless of speed. A common distractor is choice A, which confuses torque with being proportional to velocity, but torque is independent of ω in this context. When analyzing rotational motion, separate kinematic variables like ω from dynamic ones like τ and I.

Question 10

1. It becomes half as large.
2. It becomes twice as large. (correct answer)
3. It is unchanged because torque direction is unchanged.
4. It becomes zero because lower inertia means less torque needed.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, this means angular acceleration is produced by net torque and opposed by the object's rotational inertia. Reducing rotational inertia makes the object easier to accelerate rotationally, so for the same torque, α increases. Specifically, halving I while keeping τ_net constant doubles the angular acceleration. A common distractor is choice A, which reverses the relationship and claims α halves, misunderstanding inertia's inverse role. A useful strategy is to rearrange τ_net = I α to solve for α and plug in the modified values to see the outcome.

Question 11

1. Three times as large, because smaller torque means less resistance.
2. Unchanged, because $I$ is constant.
3. One-third as large, because $\alpha\propto\tau_{\text{net}}$ for fixed $I$. (correct answer)
4. Zero, because any reduction in torque stops angular acceleration.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, net torque is what causes an object to angularly accelerate, and the magnitude of that acceleration is inversely related to the object's rotational inertia. For a constant I, the angular acceleration scales directly with the net torque applied. Thus, reducing the torque to one-third while keeping I the same will reduce α to one-third its original value. A common distractor is choice A, which mistakenly claims smaller torque means less resistance and thus larger acceleration, but actually less torque means less driving force for rotation. A transferable strategy is to treat rotational dynamics like linear ones, replacing force with torque, mass with inertia, and acceleration with angular acceleration.

Question 12

1. $\alpha_2=2\alpha_1$ because more inertia means more acceleration for the same torque.
2. $\alpha_2=\alpha_1$ because they have the same torque direction.
3. $\alpha_2=\tfrac{1}{2}\alpha_1$ because $\alpha=\tau_{\text{net}}/I$. (correct answer)
4. $\alpha_2=0$ because the torque is counterclockwise.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, this equation highlights that angular acceleration results from the imbalance of torques, scaled by the object's resistance to rotation via its inertia. When two objects experience the same net torque, the one with greater rotational inertia will have a smaller angular acceleration. Doubling I while keeping τ_net constant therefore halves α, as the torque is distributed over more inertia. A common distractor is choice A, which incorrectly states more inertia leads to more acceleration, confusing inertia with a driving factor rather than resistance. For similar questions, compare scenarios using ratios from α = τ_net / I to quantify changes in angular acceleration.

Question 13

1. $\tfrac{1}{4}\alpha$
2. $\alpha$
3. $4\alpha$ (correct answer)
4. Cannot be determined without angular velocity.

Explanation: This problem requires applying Newton's second law in rotational form when rotational inertia decreases significantly. The fundamental equation τ_net = I·α rearranges to α = τ_net/I, showing angular acceleration is inversely proportional to rotational inertia for constant torque. When the rotational inertia is reduced to I/4 while maintaining the same torque, the new angular acceleration becomes α_new = τ/(I/4) = 4τ/I = 4α. The angular acceleration quadruples because we're dividing the same torque by one-fourth the original inertia. Choice A incorrectly inverts this relationship, suggesting α becomes 1/4 of its original value. Remember that reducing rotational inertia makes objects easier to accelerate rotationally, so α increases when I decreases (for constant τ).

Question 14

1. $\alpha$ doubles because torque doubled.
2. $\alpha$ halves because inertia doubled.
3. $\alpha$ is unchanged because $\alpha=\tau/I$. (correct answer)
4. $\alpha$ depends only on angular velocity, so it is unchanged.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, torque and inertia both influence angular acceleration in opposing ways: more torque increases it, more inertia decreases it. When both increase by the same factor, their effects cancel out, leaving α unchanged. In this scenario, doubling both τ and I results in α remaining the same, since α = (2τ) / (2I) = τ / I. A common distractor is choice A, focusing only on torque doubling to say α doubles, but this neglects the simultaneous increase in inertia. For analogous questions, consider the ratio of changes in τ and I, as α scales with τ / I.

Question 15

1. $\alpha$ is tripled. (correct answer)
2. $\alpha$ is unchanged because $I$ is unchanged.
3. $\alpha$ is reduced to one-third because larger torque increases resistance.
4. $\alpha$ depends on angular speed, so it stays the same.

Explanation: This question tests Newton's second law in rotational form when net torque changes. The rotational form states τ_net = I·α, which means angular acceleration is directly proportional to net torque when rotational inertia is constant. If the net torque is tripled from τ to 3τ while the rod's rotational inertia remains unchanged, then α_new = (3τ)/I = 3(τ/I) = 3α. The angular acceleration triples because it's directly proportional to the applied torque. Choice C incorrectly suggests that larger torque increases resistance, confusing cause and effect—torque causes angular acceleration, not resistance to it. To analyze rotational problems, remember that tripling the torque triples the angular acceleration when I is constant.

Question 16

1. It becomes $\tfrac{3}{2}$ times as large.
2. It becomes $\tfrac{2}{3}$ as large.
3. It becomes 6 times as large. (correct answer)
4. It is unchanged because torque and inertia both changed.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, increasing torque amplifies angular acceleration, while decreasing inertia also amplifies it by reducing resistance. The combined effect is multiplicative in the ratio τ / I. Here, tripling τ and halving I results in α becoming 6 times as large, since α' = (3τ) / (I/2) = 6 (τ / I). A common distractor is choice A, suggesting it becomes 3/2 times as large by incorrectly adding factors instead of multiplying. For problems with multiple changes, calculate the overall factor as (new τ / old τ) × (old I / new I) and apply it to the original α.

Question 17

1. $\alpha$ is unchanged because torque direction is unchanged.
2. $\alpha$ doubles because $\alpha=\tau/I$. (correct answer)
3. $\alpha$ halves because less inertia means less tendency to rotate.
4. $\alpha$ becomes clockwise because inertia decreased.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, rotational inertia represents resistance to changes in rotational motion, similar to mass in linear motion. Reducing inertia while keeping torque constant increases angular acceleration because less resistance allows faster changes in rotation. Here, halving I with constant τ doubles α, as seen from α = τ / I. A common distractor is choice C, which claims α halves because less inertia means less tendency to rotate, but this reverses the inverse relationship. A useful strategy for these problems is to rearrange τ = I α to α = τ / I and substitute the changed values to find the new acceleration.

Question 18

1. $\alpha$ decreases by 20% because inertia decreased.
2. $\alpha$ increases by 25% because $\alpha=\tau/I$. (correct answer)
3. $\alpha$ is unchanged because torque is unchanged.
4. $\alpha$ depends on angular velocity, so it cannot be determined.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, rotational inertia opposes changes in angular velocity, so decreasing it allows greater acceleration for the same torque. The inverse proportionality means a reduction in I increases α by the reciprocal factor. With I decreasing to 80% (0.8 times) and τ unchanged, α increases by 1/0.8 = 1.25 times, or 25%. A common distractor is choice A, claiming α decreases by 20% because inertia decreased, but this mistakes the inverse relationship for a direct one. A key strategy is to express changes as fractions or percentages and use α ∝ 1/I to find the percentage change in α.

Question 19

1. $\alpha$ doubles because $\alpha\propto\tau$ for constant $I$. (correct answer)
2. $\alpha$ stays the same because direction is unchanged.
3. $\alpha$ halves because larger torque reduces acceleration time.
4. $\alpha$ depends on the wheel’s angular velocity, not torque.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, torque drives rotational acceleration much like force drives linear acceleration. The magnitude of angular acceleration is directly proportional to the net torque and inversely proportional to rotational inertia, so increasing torque while keeping inertia constant increases acceleration proportionally. Here, doubling the torque with constant inertia results in α doubling, as α = τ / I. A common distractor is choice C, which claims α halves because larger torque reduces acceleration time, but this confuses acceleration with time-dependent quantities like velocity. For similar problems, always isolate the variables in τ = I α and see how changes in τ or I affect α directly.

Question 20

1. $\alpha$ becomes $\tfrac{1}{3}$ as large because $\alpha\propto\tau$. (correct answer)
2. $\alpha$ becomes 3 times as large because smaller torque acts more efficiently.
3. $\alpha$ is unchanged because the rod is already rotating.
4. $\alpha$ becomes zero because torque decreased.

Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, net torque determines how quickly an object's rotation changes, with acceleration scaling directly with torque. If torque decreases while inertia stays constant, angular acceleration decreases proportionally. Here, reducing τ to one-third with constant I makes α one-third as large, following α ∝ τ. A common distractor is choice D, suggesting α becomes zero because torque decreased, but a non-zero torque still produces acceleration, just smaller. To solve similar problems, focus on the proportional relationship α = τ / I and compute the factor by which τ changes.