Seesaws both let go simultaneously, who will tip over faster and - PDF document

Seesaws 1 Seesaws 2 Introductory Question You and a child half your height lean out over � the edge of a pool at the same angle. If you Seesaws both let go simultaneously, who will tip over faster and hit the water first? You A. The small child B. Seesaws 3 Seesaws 4 Observations about Seesaws 5 Questions about Seesaws � A balanced seesaw rocks back and forth easily � How exactly does a balanced seesaw behave? � Equal-weight children balance a seesaw � Why does the seesaw need a pivot? � Unequal-weight children don’t normally balance � Why does a lone rider plummet to the ground? � Moving heavier child inward restores balance � Why do the riders’ weights and positions matter? � Sitting closer to the pivot speeds up the motion � Why does distance from the pivot affect speed? Seesaws 5 Seesaws 6 Question 1 Physics Concept � How exactly does a balanced seesaw behave? � Rotational Inertia � Is a balanced seesaw horizontal? � A body at rest tends to remain at rest � Is a horizontal seesaw balanced? � A body that’s rotating tends to keep rotating •1

Seesaws 7 Seesaws 8 Newton’s First Law Physical Quantities of Rotational Motion � Ang. Position – an object’s orientation � A rigid object that’s not wobbling and that is free of outside torques rotates at a constant � Ang. Velocity – change in ang. pos. with time angular velocity. � Torque – a twist or spin Seesaws 9 Seesaws 10 Balanced Seesaw Question 2 � A balanced seesaw � Why does the seesaw need a pivot? � experiences zero torque � How would a pivotless seesaw move? � has constant angular velocity � It’s angular velocity is constant when it is � motionless and horizontal � motionless and tilted � turning steadily in any direction Seesaws 11 Seesaws 12 Center of Mass Seesaw’s Pivot � Point about which object’s mass balances � The seesaw needs a pivot to � A free object rotates about its center of mass � support the total weight of the seesaw and riders while its center of mass follows the path of a � prevent the seesaw from falling falling object � permit the seesaw to rotate but not translate •2

Seesaws 13 Seesaws 14 Question 3 Physical Quantities � Why does a lone rider plummet to the ground? � Ang. Position – an object’s orientation � How does a torque affect a seesaw? � Ang. Velocity – change in ang. position w/ time � Why does a rider exert a torque on the seesaw? � Torque – a twist or spin � Ang. Accel. – change in ang. velocity with time � Rotational Mass – measure of rotational inertia Seesaws 15 Seesaws 16 Newton’s Second Law Forces and Torques of Rotational Motion � An object’s angular acceleration is equal to the � A force can produce a torque torque exerted on it divided by its rotational � A torque can produce a force mass. The angular acceleration is in the same direction as the torque. torque = lever arm· force (where the lever arm is perpendicular to the force) angular acceleration = torque/rotational mass torque = rotational mass· angular acceleration Seesaws 17 Seesaws 18 The Lone Rider’s Descent Question 4 � Rider’s weight produces a torque on the seesaw � Why do the riders’ weights and positions matter? � Seesaw undergoes angular acceleration � Seesaw’s angular velocity increases rapidly � Rider’s side of seesaw soon hits the ground •3

Seesaws 19 Seesaws 20 Net Torque Balancing the Riders � The net torque on the seesaw is � Each rider exerts a torque � the sum of all torques on that seesaw � Left rider produces ccw torque (weight· lever arm) � responsible for the seesaw’s angular acceleration � Right rider produces cw torque (weight· lever arm) � If those torques sum to zero, seesaw is balanced Seesaws 21 Seesaws 22 Question 5 Mass and Rotational Mass � Why does distance from the pivot affect speed? � Rider’s part of rotational mass is proportional to � How does lever arm affect torque? � the rider’s mass � the square of rider’s lever arm � How does lever arm affect rotational mass? � Moving away from pivot dramatically increases the seesaw’s overall rotational mass! Seesaws 23 Seesaws 24 Seesaw and Rider-Distance Introductory Question (revisited) � When riders move away from pivot, You and a child half your height lean out over � the edge of a pool at the same angle. If you � the torque increases in proportion to lever arm both let go simultaneously, who will tip over � the rotational mass in proportion to lever arm 2 faster and hit the water first? � Angular accelerations decrease! � Motions are slower! You A. The small child B. •4

Seesaws 25 Summary about Seesaws � A balanced seesaw � experiences zero net torque � moves at constant angular velocity � requires all the individual torques to cancel � Force and lever arm both contribute to torque � Heavier children produce more torque � Sitting close to the pivot reduces torque •5