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SeesawsSeesaws

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Introductory QuestionIntroductory Question

You and a child half your height You and a child half your height lean out over the edge of a pool at lean out over the edge of a pool at the same angle. If you both let go the same angle. If you both let go simultaneously, who will tip over simultaneously, who will tip over faster and hit the water first?faster and hit the water first?

A.A. YouYou

B.B. The small childThe small child

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Observations about Observations about SeesawsSeesaws

A balanced seesaw rocks back and forth A balanced seesaw rocks back and forth easilyeasily

Equal-weight children balance a seesawEqual-weight children balance a seesaw Unequal-weight children don’t normally Unequal-weight children don’t normally

balancebalance Moving heavier child inward restores Moving heavier child inward restores

balancebalance Sitting closer to the pivot speeds up the Sitting closer to the pivot speeds up the

motionmotion

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5 Questions about 5 Questions about SeesawsSeesaws

How exactly does a balanced seesaw How exactly does a balanced seesaw behave?behave?

Why does the seesaw need a pivot?Why does the seesaw need a pivot? Why does a lone rider plummet to the Why does a lone rider plummet to the

ground?ground? Why do the riders’ weights and Why do the riders’ weights and

positions matter?positions matter? Why does distance from the pivot Why does distance from the pivot

affect speed?affect speed?

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Question 1Question 1

How exactly does a balanced seesaw How exactly does a balanced seesaw behave?behave? Is a balanced seesaw horizontal?Is a balanced seesaw horizontal? Is a horizontal seesaw balanced?Is a horizontal seesaw balanced?

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Physics ConceptPhysics Concept

Rotational InertiaRotational Inertia A body at rest tends to remain at restA body at rest tends to remain at rest A body that’s rotating tends to keep A body that’s rotating tends to keep

rotatingrotating

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Physical QuantitiesPhysical Quantities

Ang. Position – an object’s Ang. Position – an object’s orientationorientation

Ang. Velocity – change in ang. pos. Ang. Velocity – change in ang. pos. with timewith time

Torque – a twist or spinTorque – a twist or spin

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Newton’s First LawNewton’s First Lawof Rotational Motionof Rotational Motion

A rigid object that’s not wobbling A rigid object that’s not wobbling and that is free of outside torques and that is free of outside torques rotates at a constant angular rotates at a constant angular velocity.velocity.

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Balanced SeesawBalanced Seesaw

A balanced seesawA balanced seesaw experiences zero torqueexperiences zero torque has constant angular velocityhas constant angular velocity

It’s angular velocity is constant It’s angular velocity is constant when it iswhen it is motionless and horizontalmotionless and horizontal motionless and tiltedmotionless and tilted turning steadily in any directionturning steadily in any direction

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Question 2Question 2

Why does the seesaw need a pivot?Why does the seesaw need a pivot? How would a pivotless seesaw move?How would a pivotless seesaw move?

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Center of MassCenter of Mass

Point about which object’s mass Point about which object’s mass balancesbalances

A free object rotates about its center A free object rotates about its center of mass while its center of mass of mass while its center of mass follows the path of a falling objectfollows the path of a falling object

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Seesaw’s PivotSeesaw’s Pivot

The seesaw needs a pivot toThe seesaw needs a pivot to support the total weight of the seesaw support the total weight of the seesaw

and ridersand riders prevent the seesaw from fallingprevent the seesaw from falling permit the seesaw to rotate but not permit the seesaw to rotate but not

translatetranslate

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Question 3Question 3

Why does a lone rider plummet to Why does a lone rider plummet to the ground?the ground? How does a torque affect a seesaw?How does a torque affect a seesaw? Why does a rider exert a torque on the Why does a rider exert a torque on the

seesaw?seesaw?

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Physical QuantitiesPhysical Quantities

Ang. Position – an object’s orientationAng. Position – an object’s orientation Ang. Velocity – change in ang. Ang. Velocity – change in ang.

position w/ timeposition w/ time Torque – a twist or spinTorque – a twist or spin Ang. Accel. – change in ang. velocity Ang. Accel. – change in ang. velocity

with timewith time Rotational Mass – measure of Rotational Mass – measure of

rotational inertiarotational inertia

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Newton’s Second LawNewton’s Second Lawof Rotational Motionof Rotational Motion

An object’s angular acceleration is equal to An object’s angular acceleration is equal to the torque exerted on it divided by its the torque exerted on it divided by its rotational mass. The angular acceleration rotational mass. The angular acceleration is in the same direction as the torque.is in the same direction as the torque.

angular acceleration = torque/rotational angular acceleration = torque/rotational massmass

torque = rotational mass· angular torque = rotational mass· angular accelerationacceleration

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Forces and TorquesForces and Torques

A force can produce a torqueA force can produce a torque A torque can produce a forceA torque can produce a force

torque = lever arm· forcetorque = lever arm· force(where the lever arm is perpendicular to the force)(where the lever arm is perpendicular to the force)

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The Lone Rider’s DescentThe Lone Rider’s Descent

Rider’s weight produces a torque on Rider’s weight produces a torque on the seesawthe seesaw

Seesaw undergoes angular Seesaw undergoes angular accelerationacceleration

Seesaw’s angular velocity increases Seesaw’s angular velocity increases rapidlyrapidly

Rider’s side of seesaw soon hits the Rider’s side of seesaw soon hits the groundground

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Question 4Question 4

Why do the riders’ weights and Why do the riders’ weights and positions matter?positions matter?

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Net TorqueNet Torque

The net torque on the seesaw is The net torque on the seesaw is the sum of all torques on that seesawthe sum of all torques on that seesaw responsible for the seesaw’s angular responsible for the seesaw’s angular

accelerationacceleration

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Balancing the RidersBalancing the Riders

Each rider exerts a torqueEach rider exerts a torque Left rider produces Left rider produces ccwccw torque ( torque (weight· weight·

lever armlever arm)) Right rider produces Right rider produces cwcw torque ( torque (weight· weight·

lever armlever arm)) If those torques sum to zero, seesaw If those torques sum to zero, seesaw

is balancedis balanced

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Question 5Question 5

Why does distance from the pivot Why does distance from the pivot affect speed?affect speed?

How does lever arm affect torque?How does lever arm affect torque? How does lever arm affect rotational How does lever arm affect rotational

mass?mass?

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Mass and Rotational Mass and Rotational MassMass

Rider’s part of rotational mass is Rider’s part of rotational mass is proportional toproportional to the rider’s massthe rider’s mass the the squaresquare of rider’s lever arm of rider’s lever arm

Moving away from pivot Moving away from pivot dramatically increases the seesaw’s dramatically increases the seesaw’s overall rotational mass!overall rotational mass!

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Seesaw and Rider-Seesaw and Rider-DistanceDistance

When riders move away from pivot,When riders move away from pivot, the torque increases in proportion to the torque increases in proportion to

lever armlever arm the rotational mass in proportion to the rotational mass in proportion to

lever armlever arm22

Angular accelerations decrease!Angular accelerations decrease! Motions are slower!Motions are slower!

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Introductory Question Introductory Question (revisited)(revisited)

You and a child half your height You and a child half your height lean out over the edge of a pool at lean out over the edge of a pool at the same angle. If you both let go the same angle. If you both let go simultaneously, who will tip over simultaneously, who will tip over faster and hit the water first?faster and hit the water first?

A.A. YouYou

B.B. The small childThe small child

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Summary about SeesawsSummary about Seesaws

A balanced seesawA balanced seesaw experiences zero net torqueexperiences zero net torque moves at constant angular velocitymoves at constant angular velocity requires all the individual torques to requires all the individual torques to

cancelcancel Force and lever arm both contribute Force and lever arm both contribute

to torqueto torque Heavier children produce more torqueHeavier children produce more torque Sitting close to the pivot reduces torqueSitting close to the pivot reduces torque