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