Today’s Concepts: a) Relative motion b) Centripetal acceleration Physics 211 Lecture 3 Today’s Concepts: a) Relative motion b) Centripetal acceleration

Relative Motion What you just did Demo: tractor on paper What is Mike’s velocity relative to the ground? What you just did 08

Student Suggestion Maybe we could also try to do relative motion like this: Find the velocity of A wrt D, given the velocity of A wrt B, B wrt C, and C wrt D. I don't know - something tricky. You are flying east on an airplane, that is traveling 150 m/s due east w.r.t. the air. There is a 30 m/s wind that is traveling due west w.r.t the ground. You carry your food tray toward the back of the plane with a speed of 3 m/s w.r.t. the plane. How fast are you moving relative to the ground? A) 183 m/s B) 177 m/s C) 123 m/s D) 117 m/s Vyou,ground = Vyou,plane + Vplane,air + Vair,ground Vyou,ground = -3 m/s + 150 m/s -30 m/s = 117 m/s East 10

Prelecture 3, Question 1 (Reds POV) I find it difficult to consider one moving object in the reference frame of another, especially trying to determine which object is moving in a positive direction. 11

Prelecture 3, Question 1 (Reds POV) X = + I find it difficult to consider one moving object in the reference frame of another, especially trying to determine which object is moving in a positive direction. 11

Prelecture 3, Question 1 (Reds POV) Xo = - 12 m X = + 11

Prelecture 3, Question (Green’s POV) Red Green Green Red ball starts to the right (positive) and comes closer to green (origin) 13

Checkpoint A girl stands on a moving sidewalk that moves to the right at 2 m/s relative to the ground. A dog runs toward the girl in the opposite direction along the sidewalk at a speed of 8 m/s relative to the sidewalk. What is the speed of the dog relative to the ground? vbelt,ground = 2 m/s vdog,belt = 8 m/s A) 6 m/s B) 8 m/s C) 10 m/s 15

What is the speed of the dog relative to the ground? vbelt,ground = 2 m/s vdog,belt = 8 m/s A) 6 m/s B) 8 m/s C) 10 m/s vdog, ground = vdog, belt + vbelt, ground = (-8 m/s) + (2 m/s) = -6 m/s +x 16 9

Checkpoint A girl stands on a moving sidewalk that moves to the right at 2 m/s relative to the ground. A dog runs toward the girl in the opposite direction along the sidewalk at a speed of 8 m/s relative to the sidewalk. What is the speed of the dog relative to the girl? vbelt,ground = 2 m/s vdog,belt = 8 m/s A) 6 m/s B) 8 m/s C) 10 m/s 18

What is the speed of the dog relative to the girl? vbelt,ground = 2 m/s vdog,belt = 8 m/s A) 6 m/s B) 8 m/s C) 10 m/s Using the velocity formula: vdog, girl = vdog, belt + vbelt, girl = -8 m/s + 0 m/s = -8 m/s 21 11

Tractor Demo (moving cardboard) Which direction should I point the toy bulldozer to get it across the cardboard fastest? A) To the left B) Straight across C) To the right A B C

ACT A man starts to walk along the dotted line painted on a moving sidewalk toward a fire hydrant that is directly across from him. The width of the walkway is 4 m, and it is moving at 2 m/s relative to the fire-hydrant. If his walking speed is 1 m/s, how far away will he be from the hydrant when he reaches the other side? 1 m/s 2 m 4 m 6 m 8 m Moving sidewalk 2 m/s 4 m 23 13

If the sidewalk wasn’t moving: 1 m/s 4 m Time to get across: Dt = distance / speed = 4m / 1m/s = 4 s 24 14 14

Just the sidewalk: 2 m/s 4 m 24 15 15

Combination of motions: 1 m/s 4 m 2 m/s 25 16 16

D = (speed of sidewalk) ∙ (time to get across) = (2 m/s) ∙ (4 s) = 8 m 25 17 17

ACT Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth swims perpendicular to the flow, Ann swims upstream at 30 degrees, and Carly swims downstream at 30 degrees. Who gets across the river first? A) Ann B) Beth C) Carly Beth Ann Carly Turn river into a pool on a bus…. x y 27

Look at just water & swimmers Time to get across = D / Vy B A C D 30o 30o Vy,Beth = Vo x y Vy,Ann = Vocos(30o) Vy,Carly = Vocos(30o) 29

ACT Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth swims perpendicular to the flow, Ann swims upstream at 30 degrees, and Carly swims downstream at 30 degrees. Who gets across the river second? A) Ann B) Carly C) Both same Ann Carly Add Calculation. What angle to get straight across river? x y 31

Checkpoint (& Demo: tether ball) A girl twirls a rock on the end of a string around in a horizontal circle above her head as shown from above in the diagram. If the string breaks at the instant shown, which of the arrows best represents the resulting path of the rock? A B C D Once the string breaks, there is no longer any centripetal force exerted on the rock by the string, and so the rock continues in a straight path tangent to the point at which the string broke. Top view looking down 33

Demo: water in bucket Slide 7 : 0:50-1:10 35

Centripetal Acceleration 37

w is the rate at which the angle q changes: Angular Velocity w v = wR w is the rate at which the angle q changes: q Once around: w = Dq / Dt = 2p / T v = Dx / Dt = 2pR / T 38

v = wR Angular Velocity w Another way to see it: v dt =R dq dq R v = Rw 39

Earth’s Rotation The 666 is just a useful way to remember R_earth 6.6e6 meters. 41

Earth’s Rotation Rearth = 6.4 x 106 m.

Earth’s Rotation When standing on the equator, what is the direction of your acceleration due to the rotation of the earth? East West Toward Center of Earth Away from Center of Earth (toward sky) North 45