LECTURE 17. Prof. Paul

Transcription

1 LECTURE 17 Prof. Paul

2 Announcements Exam II, two weeks away Cumulative (you must know concepts from first exam) On your hw I just handed back, (#38) I may have INCORRECTLY stated that it s wrong to use conservation of energy here. Elastic You don t need it

3 Today Glancing collisions Angular motion (review) Linear motions related to angular motions Centripetal acceleration

4 Glancing Collisions Any collision that happens in a plane need both x and y coordinates Asteroid problem is an example of one Posted online Chapter 6, problem 38 Posted online IDENTICAL to other collisions EXCEPT you must break up x & y into components.

5 Chapter 6 problem 38 Two shuffleboard disks of equal mass, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the right at 5.00 m/s. After the collision, the orange disk moves in a direction that makes an angle of 37.0 with the horizontal axis while the green disk makes an angle of 53.0 with this axis. Determine the speed of each disk after the collision.

6 2D momentum conservation (GLANCING COLLISIONS) Strategy Find sum of changes of momentum in x-direction Find sum of changes of momentum in y-direction Think about which terms are zero (check with picture) Decide if it s Elastic, Inelastic, or perfectly inelastic Elastic: use conservation of energy & conservation of momentum Inelastic: Use conservation of momentum Perfectly inelastic: use conservation of momentum & final velocities are equal in magnitude and direction Solve equations simultaneously for unknown

7 Last time: Angular Relationships Angular displacement ΔΘ = Θ f - Θ i Angular velocity ω avg. = Δθ/Δt Angular acceleration α avg. = Δω/Δt

8 Clicker Question There are 2 points (P & Q) on a disc. Q is further from the center than P. If I spin the disc clockwise: A. P s angular velocity will be greater B. Q s angular velocity will be greater C. P & Q will have the same angular velocity Q

9 Clicker Question There are 2 points (P & Q) on a disc. Q is further from the center than P. If I spin the disc clockwise: A. P s angular velocity will be greater B. Q s angular velocity will be greater C. P & Q will have the same angular velocity Q

10 Clicker Question There are 2 points (P & Q) on a disc. Q is further from the center than P. If I spin the disc clockwise: A. P s path length will be greater B. Q s path length will be greater C. P & Q will have the same path length Q

11 Clicker Question There are 2 points (P & Q) on a disc. Q is further from the center than P. If I spin the disc clockwise: A. P s path length will be greater B. Q s path length will be greater C. P & Q will have the same path length Q

12 Clicker Question There are 2 points (P & Q) on a disc. Q is further from the center than P. If I spin the disc clockwise: A. P s linear velocity will be greater B. Q s linear velocity will be greater C. P & Q will have the same linear velocity Q

13 Clicker Question There are 2 points (P & Q) on a disc. Q is further from the center than P. If I spin the disc clockwise: A. P s linear velocity will be greater B. Q s linear velocity will be greater C. P & Q will have the same linear velocity Q

14 Marching Band clip: pinwheel html

15 Demo Which way will the ball go?

16 You try: Use physics words and Newton s laws to come up with a reason for why the ball travels the way it does.

17 Arc Length (s) Path that a point follows when moving in a circle

18 Arc Length (s) Path that a point follows when moving in a circle S = arc length r = radius

19 Tangential velocity (v t ) Magnitude and direction of instantaneous motion Tangential to circular path

20 Tangential velocity (v t ) Magnitude and direction of instantaneous motion Tangential to circular path

21 Tangential acceleration (a t ) Rate at which a point is changing velocity in the same direction as the tangential velocity

22 Rela%onship Between Angular and Linear Quan%%es Displacements s = θ r Does r change as the disc spins? No Θ S = arc length r = radius Sec%on 7.3

23 You try: Is the angular displacement formula (s =θr) consistent with the formula for Circumference? For a full circle: Θ=2π s=2πr = arclength of entire circle C=2πr C=πd

24 Rela%onship Between Angular and Linear Quan%%es Displacements s = θ r Speeds v t = ω r If the disc spins at constant angular velocity does v t change? Yes! Direc%on changes Θ r = radius Sec%on 7.3

25 Rela%onship Between Angular and Linear Quan%%es Displacements s = θ r Speeds v t = ω r Accelera5ons a t = α r Θ r = radius Sec%on 7.3

26 Rela%onship Between Angular and Linear Quan%%es Displacements s = θ r Speeds v t = ω r Accelera%ons a t = α r Remember: Every point on the rota%ng object has the same angular mo%on Every point on the rota%ng object does not have the same linear mo%on Sec%on 7.3

27 Homework Chapter 7 problems: 3, 6, 8, 11 Still putting together study groups. me if you want in!