DOST-SEI Mechanical Reasoning Reviewer: Wheels, Axles & Rotational Systems

TEACHER ABI · DOST-SEI MECHANICAL REASONING

Wheels, Axles & Rotational Systems

Reason about parts that rotate together: wheel-and-axle mechanical advantage, torque, same-shaft motion, rim distance, linear speed, and rotational tradeoffs.

5–10 minute lesson27 original questionsPrecision SVG diagramsSaves progress

LessonShortcutExamplesSkill CheckPracticeMasteryFAQ

Your reviewer status

Start with the five-form Skill Check.

QUICK REVIEW

Same rotation, different rim motion

1. Same shaft = same angular motion
Rigidly connected wheel and axle turn through the same angle, same number of revolutions, and same rpm.

2. Same direction
A wheel and axle fixed to one shaft rotate in the same direction.

3. Different rim distances
In one revolution, distance traveled at a rim is 2πr. The larger radius covers more distance.

4. Different linear speeds
For the same angular speed, v=rω. Points farther from the axis move faster.

5. Torque grows with radius
For a tangential force, τ=Fr. Applying the same force farther from the axis gives more torque.

6. Wheel-and-axle IMA
When effort is applied at the wheel, IMA = wheel radius ÷ axle radius.

DO IT FAST

SAME ANGLE → CHECK RADIUS → BALANCE TORQUE

SAME ANGLE: parts fixed to one shaft have the same rotation. CHECK RADIUS: larger radius means greater rim distance and linear speed. BALANCE TORQUE: for ideal equilibrium, effort force × effort radius = load force × load radius.

WORKED EXAMPLES

Read the axis before the numbers

1. Same shaft

If the wheel makes 5 turns, the axle also makes 5 turns.

2. Mechanical advantage

Wheel radius 40 cm, axle radius 10 cm: IMA = 40/10 = 4.

3. Torque balance

A 60 N load on a 10 cm axle needs only 20 N at a 30 cm wheel because 20×30 = 60×10.

4. Rim distance

Both points make one revolution, but the outer point travels farther because its circular path is larger.

5. Winch transfer

A long crank can create a larger drum force because the effort acts at a larger radius.

Common traps

Thinking the smaller axle spins faster: not when it is rigidly fixed to the same shaft. Confusing angular speed with linear speed: same rpm does not mean same rim speed. Reversing the IMA ratio: with effort at the wheel, use wheel radius ÷ axle radius. Using diameter on one side and radius on the other: keep the measure consistent. Forgetting torque: force alone does not determine turning effect; radius matters.

FIVE-FORM SKILL CHECK

Can you transfer the idea across five forms?

This diagnoses your next practice step; it does not verify mastery.

CHOOSE YOUR PRACTICE

Practice at the level you need

FRESH MASTERY CHECK

Verify the competency

Mastery requires 5/5. An unsuccessful attempt loads a different set.

FAQ

Quick clarifications

Does the smaller axle rotate faster than the wheel?
No—not if they are rigidly fixed to the same shaft. Their rpm is identical.

Then what changes with radius?
Rim distance, linear speed, and torque leverage change.

When is IMA = R/r?
For the ideal wheel-and-axle arrangement where effort is applied at the larger wheel and the load acts at the smaller axle.

Why does a longer handle help?
It increases the perpendicular distance from the axis, producing more torque for the same force.

RELATED COMPETENCIES

Continue Mechanical Reasoning

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Original Teacher Abi practice for DOST-SEI preparation. Independent and not affiliated with DOST-SEI.