Physics 218

Alexei Safonov

Lecture 6: Kinematics in 2/3-D

Chapter 3, continued

• Kinematics in Two or Three Dimensions–Relative Motion–Circular Motion

Football Punt• A football is kicked at angle Q0 with a

velocity V0. The ball leaves the punters foot h meters above the ground. – The velocity at the maximum height– How far does it travel, in the X direction, before

it hits the ground?– What angle maximizes the distance traveled

h

Relative Motion

What you just did bcabac vvv

A) Because the girl is actually moving and the two vectors are opposite, so together they make 6 m/s

B) Because the girl is not moving relative to the belt, and the dog is going 8 m/s relative to the belt, the dog is also moving 8 m/s relative to the girl..

C) The dog and girl are running towards each other so when you add the two velocities together it would be 8+2.

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

A) Because the girl is actually moving and the two vectors are opposite, so together they make 6 m/s

B) Because the girl is not moving relative to the belt, and the dog is going 8 m/s relative to the belt, the dog is also moving 8 m/s relative to the girl..

B) Because the girl is not moving relative to the belt, and the dog is going 8 m/s relative to the belt, the dog is also moving 8 m/s relative to the girl.

Using the velocity formula:vdog, girl = vdog, belt + vbelt, girl

= -8 m/s + 0 m/s = -8 m/s

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

1 m/s

4 m

2 m/s

Combination of motions:

hydrantsidewalksidwalkmanhydrantsidewalk vvv ,,,

A

B

C

Vy,Beth = Vo

30o 30o

Vy,Ann = Vocos(30o)

Vy,Carly = Vocos(30o)

Time to get across = D / Vy

D

Look at just water & swimmers

x

y

Uniform Circular Motion

• Fancy words for moving in a circle with constant speed

• We see this around us all the time– Moon around the earth– Earth around the sun– Merry-go-rounds

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

Top view looking down

CheckPoint

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

Top view looking down

After the string breaks, the rock will have no force acting on it, so it cannot accelerate. Therefore, it will maintain its velocity at the time of the break in the string, which is directed tangent to the circle.

CheckPoint

Uniform Circular Motion - Velocity

• Velocity vector = |V| tangent to the circle

• Is this ball accelerating?–Why?

Centripetal Acceleration

• Vector difference V2 - V1 gives the direction of acceleration a

dtvvdtvda /)(/ 12

a

R

Centripetal Acceleration

• Need to know a bit more math to calculate the magnitude, so for now just memorize:

• Centripetal acceleration: |a|=v2/R

dtvvdtvda /)(/ 12

a

R

Centripetal Acceleration

Centripetal Acceleration

Speed = distance/timeDistance in 1 revolution divided by the

time it takes to go around once

Speed = 2pr/TNote: The time to go around once is known as the Period, or T

Circular Motion: Get the speed!