FULL REVIEW
Full Review — Newton's Laws of Motion — Calculus-Based
Review the essential ideas, relationships, and problem-solving tools for Newton's Laws of Motion.
TIME
45–60 minutes
BEST FOR
A complete topic review
FINISH WITH
A readiness check
After this full review, you'll be able to...
recall the essential ideas, apply them to representative problems, and determine what to study next.
Choose how you want to review
Course Alignment
This Physics Sensei Topic Review is an independent learning resource. Use it to reinforce key concepts, prepare for homework, or review before a quiz or exam.
Related Unit Review: If you need to review the complete unit material, review Newton's Laws and Free-Body Diagrams here →
RESOURCE: Physics Sensei Topic Review | TOPIC ID: MEC-U05-T01 | TOPIC: Newton's Laws of Motion | PARENT UNIT: MEC-U05 — Newton's Laws and Free-Body Diagrams | COURSE LEVEL: Calculus-Based
BEST USED ✓ After learning the topic ✓ Before starting homework ✓ Before a quiz or exam
Your Review Plan
Complete these six stages in order. Each stage builds on the previous one and prepares you for the final readiness check.
6 Stages • Approximately 45–60 minutes.
Warm-Up Check
Before you begin, take a moment to see what you already remember. Do not worry about getting everything right. This is only a starting point.
ACTIVITY 1
Warm-Up 1
Answer before revealing the response.
State Newton's second law in momentum form.
Reveal Answers
∑𝐅 = d𝐩/dt.
Why it works: Connect the motion statement to the net external force or interaction pair.
ACTIVITY 2
Warm-Up 2
Answer before revealing the response.
If v(t) is constant, what are a and ∑F for constant mass?
Reveal Answers
a = d𝐯/dt = 0 and therefore ∑𝐅 = 0.
Why it works: Connect the motion statement to the net external force or interaction pair.
ACTIVITY 3
Warm-Up 3
Answer before revealing the response.
For an interaction A–B, write the vector relationship between the two third-law forces.
Reveal Answers
𝐅(A→B) = −𝐅(B→A).
Why it works: Connect the motion statement to the net external force or interaction pair.
Ready to strengthen your understanding?
You've refreshed what you already know. Next, you'll reinforce the essential concepts that will help you solve problems with confidence. Need to see the learning path again?
Core Concepts
Let's rebuild the key ideas one step at a time. Focus on understanding the relationships before worrying about solving problems.
KEY CONCEPT 1
Newton's First Law and Inertia
The net external force equals the time derivative of momentum. For constant mass, this becomes m d𝐯/dt. Zero net force means constant momentum.
∑F = 0 → a = 0
Example: Check the net force on one object before deciding how motion changes.
Sensei note: Constant velocity does not require rest.
KEY CONCEPT 2
Newton's Second Law: Net Force and Motion
Third-law forces are simultaneous interaction forces on different bodies. The pair is equal and opposite even when accelerations differ.
∑𝐅 = d𝐩/dt; for constant mass, ∑𝐅 = m d𝐯/dt = m𝐚
Example: Use object labels on interaction forces.
Sensei note: Weight and normal are not a third-law pair.
KEY CONCEPT 3
Newton's Third Law: Interaction Pairs
Newton's third law is a vector statement about one interaction. Equal forces can produce different accelerations because the masses differ.
𝐅(A→B) = −𝐅(B→A)
Example: Compare force direction with acceleration or momentum-change direction.
Sensei note: Equal third-law forces can produce different accelerations.
Ready to apply these ideas?
You've reinforced the essential concepts. Now it's time to put them into practice by working through guided examples and building your problem-solving confidence. Need a quick reminder?
Guided Practice
Now it's time to apply what you've reviewed.
Work through each activity in order. The examples become gradually more challenging, and each one prepares you for the final readiness check.
PRACTICE 1
Practice 1
Solve and justify your Newton's-law reasoning.
A 2.0 kg particle has v(t) = (t³ i + 2t j) m/s. Find F(t) and evaluate at 2.0 s.
Reveal Answers
a(t) = (3t² i + 2 j) m/s²; F(t) = (6t² i + 4 j) N; at 2.0 s, F = (24 i + 4 j) N.
Why it works: Isolate the object, determine the net force, then connect it to motion.
PRACTICE 2
Practice 2
Solve and justify your Newton's-law reasoning.
Two skaters exert a third-law force pair of 120 N. For masses 60 kg and 40 kg, compare acceleration magnitudes.
Reveal Answers
The 60 kg skater has 2.0 m/s²; the 40 kg skater has 3.0 m/s².
Why it works: Isolate the object, determine the net force, then connect it to motion.
PRACTICE 3
Practice 3
Solve and justify your Newton's-law reasoning.
A 3.0 kg particle has r(t) = (2t³ i − t² j) m. Find a(t) and F(t).
Reveal Answers
a(t) = (12t i − 2 j) m/s²; F(t) = (36t i − 6 j) N.
Why it works: Isolate the object, determine the net force, then connect it to motion.
Ready to check your understanding?
You've practiced the essential skills with guidance. Now it's time to solve a few short problems on your own and confirm you're ready to move forward. Need a quick reminder?
Confidence Check
You've rebuilt the key ideas and practiced them with guidance. Now try these short questions on your own to check your understanding before moving on.
QUICK CHECK 1
Newton's Laws Check 1
Solve and justify your conclusion.
If p(t)=(4t i−t² j) kg·m/s, find F(t).
Reveal Answers
F(t)=(4 i−2t j) N.
Why it works: Use the correct object and distinguish net-force effects from third-law pairs.
QUICK CHECK 2
Newton's Laws Check 2
Solve and justify your conclusion.
Can a third-law pair produce different acceleration magnitudes? Explain.
Reveal Answers
Yes. Equal force magnitudes with different masses give different accelerations.
Why it works: Use the correct object and distinguish net-force effects from third-law pairs.
QUICK CHECK 3
Newton's Laws Check 3
Solve and justify your conclusion.
A 100 kg object and a 25 kg object exert a 200 N pair. Compare accelerations.
Reveal Answers
2.0 m/s² and 8.0 m/s².
Why it works: Use the correct object and distinguish net-force effects from third-law pairs.
How did it go?
You've checked your understanding. Take one final look at the essential ideas before deciding what to do next. Need a quick reminder?
Summary
Before moving on, take one final look at the most important ideas from this review.
KEY TAKEAWAY 1
Key Takeaway 1
Zero net force means no change in velocity.
KEY TAKEAWAY 2
Key Takeaway 2
Net external force determines acceleration or momentum change.
KEY TAKEAWAY 3
Key Takeaway 3
Third-law forces are equal/opposite and act on different objects.
MY ONE-SENTENCE SUMMARY
In my own words, the most important idea is:
____________________________________________
Ready for your next step?
You've reviewed the essential ideas one last time. Now choose the resource that best matches how confident you feel. Need a quick reminder?
Next Step
Great work!
You've completed this review. Choose the next resource that best matches how confident you feel.
I'm Still Unsure
Review the key ideas and examples again.
Review Again →
I Need More Practice
Continue with additional practice for this topic.
Go to Practice →
I'm Ready
Continue to the next recommended resource.
Continue →