FOCUSED REVIEW
Focused Review — Static Equilibrium and Stability — Algebra-Based
Reinforce the highest-leverage ideas and representative problem-solving tools for Static Equilibrium and Stability.
TIME
Approximately 15 minutes
BEST FOR
Targeted reinforcement
FINISH WITH
A readiness check
After this focused review, you'll be able to...
reinforce the key relationships, apply them to representative problems, and identify what still needs work.
Choose how you want to review
Course Alignment
This Physics Sensei Unit Review is an independent learning resource. Use it to reinforce key concepts, prepare for homework, or review before a quiz or exam.
RESOURCE: Physics Sensei Unit Review | UNIT ID: MEC-U23 | TOPIC: Static Equilibrium and Stability | COURSE LEVEL: Algebra-Based
BEST USED ✓ After learning the unit ✓ 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 15 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
Key Equations
Answer before revealing the response.
Write the static-equilibrium equations for a planar rigid body.
Reveal Answers
ΣFx = 0, ΣFy = 0, and Στ = 0.
Why it works: This checks a prerequisite idea used in the equilibrium and stability review.
ACTIVITY 2
Torque Direction
Answer before revealing the response.
A downward force acts to the right of a pivot. Is its torque clockwise or counterclockwise?
Reveal Answers
Clockwise.
Why it works: This checks a prerequisite idea used in the equilibrium and stability review.
ACTIVITY 3
Quick Application
Answer before revealing the response.
A 50 N force is perpendicular to a 0.40 m lever arm. Find the torque magnitude.
Reveal Answers
τ = rF = (0.40 m)(50 N) = 20 N·m.
Why it works: This checks a prerequisite idea used in the equilibrium and stability review.
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
Reinforce the two highest-leverage relationships, then use them in representative situations.
KEY CONCEPT 1
Force Equilibrium
Resolve forces into components and require the sum in each independent direction to be zero. In two dimensions, this normally gives ΣFx = 0 and ΣFy = 0.
ΣFx = 0 and ΣFy = 0
Example: A hinge force may have both horizontal and vertical components.
Sensei note: Draw the free-body diagram before writing equations.
KEY CONCEPT 2
Torque Equilibrium
Choose an origin and require Στ = 0. Use τ = rF sin θ, or use the perpendicular lever arm directly. A strategic origin can remove unknown forces from the torque equation.
Στ = 0 and τ = rF sin θ
Example: Taking torques about a hinge eliminates both hinge-force components from that equation.
Sensei note: Assign one rotational direction positive and keep the sign convention consistent.
KEY CONCEPT 3
Stability and Tipping
For an object resting on a base, tipping begins when the line of action of the weight reaches a support edge. Before that point the normal-force distribution can adjust to maintain equilibrium; beyond it, the weight creates a net tipping torque.
At tipping, the weight line reaches the support edge.
Example: A wider base increases the horizontal displacement required for the weight line to reach the edge.
Sensei note: At the tipping threshold, treat the edge as the pivot.
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
Apply the reinforced ideas to two representative situations, then use the strategy card to check your setup.
PRACTICE 1
Right Support Reaction
Take torques about the left support.
A 6.0 m uniform beam of weight 300 N is supported at both ends. A 600 N load is 2.0 m from the left support. Find the right support force.
Reveal Answers
Take torques about the left support: R(6.0) − 300(3.0) − 600(2.0) = 0. Thus R = 350 N.
Why it works: Torque balance about the left support isolates the right reaction.
PRACTICE 2
Left Support Reaction
Use vertical force balance after the right reaction is known.
For the previous beam, find the left support force.
Reveal Answers
Vertical force balance gives L + 350 − 300 − 600 = 0, so L = 550 N.
Why it works: The vertical reactions must balance the total downward load.
PRACTICE 3
Cable-Supported Beam
Take torques about the hinge.
A 2.0 m ladder-like beam of weight 120 N is horizontal, hinged at one end, and supported by a cable making 60° with the beam at the other end. Find the cable tension.
Reveal Answers
Torque balance about the hinge: T(2.0)sin 60° − 120(1.0) = 0. Thus T ≈ 69 N.
Why it works: The hinge force contributes no torque about the hinge, leaving the cable and beam weight.
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
Cable Tension
Solve using torque equilibrium.
A 4.0 m horizontal uniform beam weighs 200 N and is hinged at the left end. A vertical cable at the right end holds it. Find the cable tension.
Reveal Answers
T(4.0) − 200(2.0) = 0, so T = 100 N.
Why it works: Taking torques about the hinge removes the hinge-force components.
QUICK CHECK 2
Angled Force Torque
Calculate the torque magnitude.
A 80 N force acts at 30° to a 0.50 m lever arm. Find the torque magnitude.
Reveal Answers
τ = (0.50)(80)sin 30° = 20 N·m.
Why it works: Only the perpendicular component of the force produces torque.
QUICK CHECK 3
Support Reactions
Use force balance after finding one reaction.
A 5.0 m light beam supports a 500 N load 1.0 m from the left end and is supported at both ends. Find both support forces.
Reveal Answers
Right: R(5.0) = 500(1.0), so R = 100 N. Left: L = 400 N.
Why it works: Torque balance gives one reaction; vertical force balance gives the other.
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
Use all equilibrium equations
Static equilibrium requires component force balance and torque balance.
KEY TAKEAWAY 2
Choose the pivot strategically
A good pivot choice can eliminate unknown forces and simplify the algebra.
KEY TAKEAWAY 3
Tipping is a torque problem
At the tipping threshold, the support edge becomes the pivot and the normal force acts through that edge.
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
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