AP Physics Monday 15.03.16 Standards: Warm Up Find the final angular speed and the angular displacement of the (r= 0.01 m) tires of a toy car if the car is moving at 2 m/s initially and accelerates at a rate is 6 m/s2 for two seconds. Week 28 P-Problem Solvers Standards: 4D net torque changes angular momentum of system RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT distinguish rotational inertia from linear inertia. Agenda: Warm Up Collect HW Moment of Inertia Notes & Demo HW Tap#14 Moment of Inertia Homework Tap#14

AP Physics Tuesday 15.03.17 Standards: Warm Up What two factors affect the rotational inertia of a spinning object? D-Disciplined Learners Standards: 4D net torque changes angular momentum of system RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT recognize the factors that increase the rotational inertia of an object. Agenda: Warm Up Review HW Finish Moment of Inertia Activity Homework

AP Physics Wednesday 15.03.18 Warm Up A car with 60.0 cm rims is moving ahead at a speed of 12.0 m/s. Find the angular speed, period, and frequency of the tires. E-Effective Communicators Standards: 4D net torque changes angular momentum of system RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT use the rotational equations of motion to find the angular acceleration of a marble rolling down the ramp. 3.0 m/s to the right Agenda: Warm Up #13 Golf ball vs Marble Homework

AP Physics Thursday 15.03.19 Standards: Warm Up What is the angular momentum of 4kg object rotating with a tangential speed of 6m/s at a radius of 2m from its pivot point? What would its linear momentum be if the object was severed from its pivot? P-Problem Solvers Standards: 4D net torque changes angular momentum of system I –Independent Resilient Individuals RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT use the rotational equations of motion to find the angular acceleration of a marble rolling down the ramp. Agenda: Warm Up Rotational Energy & its Conservation Lab Homework Tap#15 AP Problem

AP Physics Friday 15.03.20 Standards: Warm Up If a force causes a 2.0kg mass on the end of a 4.0m string to have an increase in its angular velocity of 4.0 rad/s over a 2.0 second time period. What would be the torque experienced by the mass. P-Problem Solvers Standards: 4D net torque changes angular momentum of system RST.11-12.9 Synthesize information from a range of sources into coherent understanding of a process, phenomenon, or concept,… WHST.11-12.7: research to aid in problem solving Learning Goal: SWBAT determine how a rolling objects shape and radius affects its translational motion. Agenda: Warm Up Review AP Torque & Angular Momentum Problem Rotational Energy & its Conservation Lab Rotational Motion Test Wednesday Homework Tap#16 – AP Problem

Linear VS Rotational Equations of Motion Concept Linear Rotational *Note: The x in rotational motion means position on the circle. More generally the equation is written s=rθ and in fact all of the linear and rotational motion equations would use an s for displacement in its most general form. * x Position θ, Displacement , Velocity Acceleration , Equation of Motion #1 Equation of Motion #2 Equation of Motion #3 Extra Credit: Use the equations for rotational position,velocity & acceleration to convert the Linear Equations of Motion into the Rotational Motion Equations.

#9 Center of Mass Lab Activity 1. Find the center of mass of a 100 g mass at the 75 cm mark and a 200 g mass at the 25 cm mark. Will there be a net Torque associated with this center of mass? Calculate the net Torque at the center of mass. 2. Take a 20g and 40g mass. If the pivot point is at the 50 cm mark on the ruler and the 20g mass is placed at the 70 cm mark, where should you put the 40g mass to make the center of mass hit the pivot point. Calculate, then check your work by testing out your calculated position. 3. Take a 10 g mass. Place the 10g mass on the 80 cm mark. Where should you make the pivot point so that it touches the center of mass and the ruler balances? Calculate then test with a ruler and masses. 4. A 100 g mass is at the 90cm mark on a ruler that pivots at the 50 cm mark. A 500 g mass is at the 30 cm mark on the same ruler. Where would a 200 g mass need to be placed to make the center of mass hit the 50 cm mark. Calculate then verify.

Tap#8 & #9 & #10 & #11 see sheet

Rotational Motion of Tumblebuggy Activity #12 We understand the linear motion of a tumblebuggy, but lets also describe the angular component of motion on the tumblebuggy. Find the speed of the tumblebuggy. Find the angular speed of each of the tumblebuggy wheels. Find the frequency and period of rotational of the tumblebuggy tires. How many rpm’s does the tumblebuggy produce? Write a paragraph explaining how you might attempt to find the torque produced by the wheels. Include the information and the devices you would need to use in order to measure it.

#13 Angular Acceleration Lab You will revisit the motion of objects accelerating down a ramp. Engage: Golf Ball vs Marble Rotational Motion Racing Match -Predict: Will a golf ball or a marble contain a greater angular acceleration? Will their final linear velocities be the same or different? Test: Your Objective is to compare the angular acceleration and final velocity of a golf ball vs. the marble. Object Mass (kg) distance (m) time1 (s) time2 (s) time3(s) tave(s) radius ( r ) final velocity (m/s) final angular velocity (rad/s) linear acceleration (m/s2) angular acceleration (rad/s2) Marble Golf Ball Interpret: What are your results? Do they seem reasonable? Explain the physics in a paragraph.

#14 Angular Acceleration Lab 1a. Predict which dowel has more rotational inertia? 1b. Predict Which ball has more Test Each Prediction Gradually reduce the radius of the circle that the golf and ping pong ball make. Is it easier or harder to spin? is the rotational inertia bigger or smaller for smaller radius’s? Find the rotational inertia of each object using the formulas on the back of your new sheet. I ball on string= mr2 Idowel = ½ mr2 Fat Dowel m r Skinny Dowel Ping Pong Ball Golf Ball

#15 Rotational Inertia by Rolling Lab Theory: When an object rolls, it has kinetic energy both in its linear (translational) motion and its rotation. The distribution of the mass about the body can affect how much energy is required to cause the spin. For example, a cart with very small wheels has almost none of its kinetic energy distributed in rolling whereas a thin hoop has a large share of its mass moving at the radial distance. In the case of an object rolling down a ramp from rest, the Total Kinetic Energy is equal to the change in gravitational potential energy ΔU=mgΔh. The total kinetic energy of a body is found by Ktotal=Ktrans+Krot=1/2 mv2+ ½ Iω2 v0=0 d v=rω h1 h2 The new symbols, I and ω, are rotational inertia and angular velocity, respectively. Where I is a constant for rigid bodies and depends on how the mass is distributed, it is usually stated as CmR2 where C is a constant between zero and 1. Angular velocity is easily found by measuring the objects velocity and converting by the formula V=Rω. Procedure: Raise a table on one side by putting a block of wood or a book under two of its legs. Allow objects of various shapes and mass distributions to roll a distance of 1.5 meters across the tilted surface. The change in height is easily measured by comparing h1 to h2 as shown. Timing the journey allows one to calculate the average translational speed, and from that the angular speed. Vaverage=1/2 (V+V0). The higher rotational inertias become evident when more energy is in the rotation. This causes a slower translational verlocity and a longer rolling time. Data: Start by measuring 1.5 m on the table top. Raise the table with the wood blocks and determine the change the height over those 1.5 m. Δh=_________ m Time the cart as it travels through this distance, fill in the chart on the next page. *** Repeat your trials until the time value is reliable.

As you do the trials make sure to predict whether the object will roll faster or slower than the previous object. DO AT LEAST 4 Objects mass Radius d (m) time (s) Vave=d/t Vf=2Vavg ω=vf/R Ktotal= mgΔh Ktrans= ½ mv2 Krot= Ktot-Ktrans Rot. Inertia: Krot/2ω2 C= I/(mR2) hot wheel 1.5 blue cart tape cylinder cap cylinder solid squish ball ping pong ball marble solid foam disk thick dowel think dowel

Analysis 1. Create a list that Organizes the objects in order of rotational inertia, from largest to smallest. 2. Use conservation of energy to show that neither mass nor radius is needed to predict the final velocity. 3. Is #2 verified by experiment? For example, do both solid cylinders have the same roll time? Can you understand that a disc is a solid cylinder and that a ring is a hollow cylinder? Do rings and cylinders have the same fall time? Do disks and rings have the same fall time? #2 & #4 suggest they shoul. Expected values for C are 1 ring/hoop/tube, ½=disc/cylinder, 2/5 solid sphere, 2/3=hollow sphere. How well (in percent) do your values match these expected values? What would roll down a hill faster, a hard-boiled egg, a fresh egg, or a hollow plastic Easter egg? Explain. Imagine you are at the store buying foods in cans. Would chicken broth roll down a hill faster than an empty can? What about pumpkin pie mix (sticky & thick)? What was cart the fastest object today? An object that is at rest, not spinning, will not spin unless acted on by an outside torque. Knowing that a torque is a force that acts at a radius, what force was causing the torque? What made the objects spin? If this force was absent what would their movement be like? What are the likely sources of error that could make our measurement unreliable? How well did the experiment work ( see#6) Write a conclusion.