... of objects in 3-D under constant acceleration (problem in projectile motion) ... If projectile begins and ends at same height, maximum distance is achieved for Q ...

**Title: Announcements:** ** 1** Announcements

Physics Learning Resource Center Open, gt room P207-C Open 9am - 5 pm Monday - Friday Hours also listed on www.phys.uconn.edu NOTE Homework 1 (due this Fri. 9/8 by 500 pm EST on WebAssign) Homework 2 (due next Fri. 9/15 by 5.00 pm) ** 2** Physics 151 Lecture 5Todays Agenda(Chapter 4)

Projectile motion Uniform circular motion text sections 4.1-4.5 ** 3** ACT -1Question from past Exam-1 Two balls, projected at different times so they dont collide, have trajectories A and B, as shown.

Which statement is true. Initial speed of ball B must be greater than that of ball A. Ball A is in the air for a longer time than ball B. Ball B is in the air for a longer time than ball A. Ball B has a greater acceleration than ball A. None of above. ** 4** Review Kinematics in 3D (2D)

Motion of objects in 3-D under constant acceleration (problem in projectile motion) -gt independence of x- and y- components y y0 v0y t - 1/ 2 g t2 vy v0y - g t ? to 0 Animation (v) Animation (a) x vx t vx v0x

** 5** Review Kinematics in 3D (2D) (cont.)

How many parameter determine projectile motion ? at to 0 xo, yo , vox, voy we have 4 equations ! 9 variables plus ag at t t x(t) , y(t), vx, vy 4 independent variables !

** 6** Projectile Motion g v0 Q Typical Questions, 1. Dx How far will it go ? 2. Dy How high will it be at some distance ? 3. t How long until it hits ? 4. Q At what angle should I start ? 5. v0 How fast must I start ?

** 7** Projectile Motion g v0 Q

Useful Things to Know If projectile begins and ends at same height, maximum distance is achieved for Q 45. (prove it) x distance is same for angles about 45 if everything else remains the same. Time in flight depends on y equation if no barriers other than the earth interrupt the flight path. ** 8** Projectile Motion / Example Problem v0 g Q UConn football team wants to complete a 45m pass (about 50 yards). Our qb can throw the ball at 30 m/s. At what angle must he throw the ball to get it there ? SOLUTION Q 15 or 75 which gets there first ?

** 9** Problem 3 (correlated motion of 2 objects in 3-D)

Suppose a projectile is aimed at a target at rest somewhere above the ground as shown in Fig. below. At the same time that the projectile leaves the cannon the target falls toward ground. t t1

** 10** Review( displacement, velocity, acceleration ) Velocity Acceleration

** 11** General 3-D motion with non-zero acceleration because either or both Animation

Uniform Circular Motion is one specific case of this ** 12** Uniform Circular Motion See text 4-4

What does it mean ? How do we describe it ? What can we learn about it ? ** 13** What is Uniform Circular Motion (UCM) ? See text 4-4

Motion in a circle with Constant Radius R Constant Speed v v acceleration ? ** 14** How can we describe UCM? See text 4-4

In general, one coordinate system is as good as any other Cartesian (x,y) position (vx ,vy) velocity Polar (R,?) position (vR ,?) velocity In UCM R is constant (hence vR 0). ? (angular velocity) is constant. Polar coordinates are a natural way to describe UCM! y v (x,y) R ? x

** 15** Polar Coordinates See text 4-4

The arc length s (distance along the circumference) is related to the angle in a simple way s R?, where ? is the angular displacement. units of ? are called radians. For one complete revolution 2?R R?c ?c 2? ??has period 2?. ** 16** Polar Coordinates...

In Cartesian co-ordinates we say velocity dx/dt v. x vt In polar coordinates, angular velocity d?/dt ?. ? ?t ? has units of radians/second. Displacement s vt. but s R? R?t, so y v R s ???t x

** 17** Period and Frequency

Recall that 1 revolution 2? radians frequency (f) revolutions / second (a) angular velocity (?) radians / second (b) By combining (a) and (b) ? 2? f Realize that period (T) seconds / revolution So T 1 / f 2?/? ** 18** Lecture 5, ACT 2Uniform Circular Motion

A fighter pilot flying in a circular turn will pass out if the centripetal acceleration he experiences is more than about 9 times the acceleration of gravity g. If his F18 is moving with a speed of 300 m/s, what is the approximate diameter of the tightest turn this pilot can make and survive to tell about it ? ** 19** Acceleration in UCM

This is called Centripetal Acceleration. Now lets calculate the magnitude But ?R v?t for small ?t

** 20** Lecture 5, ACT 2Uniform Circular Motion

A fighter pilot flying in a circular turn will pass out if the centripetal acceleration he experiences is more than about 9 times the acceleration of gravity g. If his F18 is moving with a speed of 300 m/s, what is the approximate diameter of the tightest turn this pilot can make and survive to tell about it ? (a) 20 m (b) 200 m (c) 2000 m (d) 20,000 m ** 21** Recap for today

Recap of Projectile Motion Introduce Uniform Circular Motion Reading assignment for Monday Reread Circular Motion Ch 4.4-4, pp.91-95 Read Relative Velocity Ch 4.5, pp.95-99 Homework 1 (due this Fri. 9/8 by 500 pm EST on WebAssign) Problems from Chapter 1 and 2 Homework 2 (due next Fri. 9/15 by 5.00 pm) Problems from Chapter 3 and 4