Lecture 03: Relative and Circular Motion

Physics 2210Fall Semester 2014

Announcements

● Homeworks due 11:59 PM Tues/Thurs ● Schedule next few weeks:

● 9/08 – Unit 3● 9/10 – Unit 4● 9/15 – Unit 5● 9/17 – Unit 6● 9/22 – Unit 7, Exam Review● 9/24 – Exam 1, Units 1-6

Mechanics Lecture 2, Slide 3

Monkey Troubles

You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting?

A) Right at the monkeyB) Below the monkeyC) Above the monkey

Mechanics Lecture 2, Slide 4

Monkey

x = xo

Dart

x = vo t

2

2

1gty −=

Shooting the Monkey…

2

2

1gty −=

Mechanics Lecture 2, Slide 5

Shooting the Monkey…

y = voy t − 1/2 g t 2

Still works even if you shoot upwards!

y = yo − 1/2 g t 2

Dart hits themonkey

Mechanics Lecture 2, Slide 6

Monkey Troubles

You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting?

A) Right at the monkeyB) Below the monkeyC) Above the monkey

Mechanics Lecture 3, Slide 7

Classical Mechanics Lecture 3

Today’s Concepts:a) Relative motionb) Centripetal acceleration

“Lecture Thoughts” Responses● Numerical Examples!● Reference frames

● Sign conventions● Graphing

● Centripetal acceleration● Derivations● Angular velocity

Relative Motion

On your equation sheet...

Mechanics Lecture 3, Slide 9

Relative Motion

What is vMike,Ground

?

Follow-up: How would the previous problem change if Mike were running at 3 m/s with

respect to the train, to the left?

Mechanics Lecture 3, Slide 11

Prelecture 3, Question 1

Mechanics Lecture 3, Slide 12

Prelecture 3, Question 1

Mechanics Lecture 3, Slide 13

vbelt,ground = 2 m/s

vdog,belt = 8 m/s

A) 6 m/s B) 8 m/s C) 10 m/s

CheckPoint:What is the speed of the dog relative to the ground?

Mechanics Lecture 3, Slide 14

vdog, ground = vdog, belt + vbelt, ground

= (−8 m/s) + (2 m/s) = −6 m/s

+x

vbelt,ground = 2 m/s

vdog,belt = 8 m/s

What is the speed of the dog relative to the ground?

A) 6 m/s B) 8 m/s C) 10 m/s

Mechanics Lecture 3, Slide 15

CheckPoint

What is the speed of the dog relative to the woman?

vbelt,ground = 2 m/s

vdog,belt = 8 m/s

A) 6 m/s B) 8 m/s C) 10 m/s

Mechanics Lecture 3, Slide 16

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

B) Because she 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 her C) The dog and woman 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 woman?

vbelt,ground = 2 m/s

vdog,belt = 8 m/s

A) 6 m/s B) 8 m/s C) 10 m/s

Mechanics Lecture 3, Slide 17

Flashcard Question

Moving sidew

alk

2 m/s

1 m/s

4 m

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?

A) 2 m

B) 4 m

C) 6 m

D) 8 m

Mechanics Lecture 3, Slide 18

Flashcard Question

Moving sidew

alk

2 m/s

1 m/s

4 m

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?

A) 2 m

B) 4 m

C) 6 m

D) 8 m

Mechanics Lecture 3, Slide 19

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

x

y

AnnBeth

Carly

Flashcard Question

Mechanics Lecture 3, Slide 20

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

x

y

AnnBeth

Carly

Flashcard Question

Mechanics Lecture 3, Slide 21

x

y

Flashcard Question

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

Mechanics Lecture 3, Slide 22

x

y

Flashcard Question

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

Centripetal Acceleration

Mechanics Lecture 3, Slide 24

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 (& Demo)

Mechanics Lecture 3, Slide 25

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 (& Demo)

Mechanics Lecture 3, Slide 26

Centripetal Acceleration

Example: What is the angular speed of the Earth as it rotates about its axis? What is the linear speed of a person on the equator, due to the Earth's motion? What about in Salt Lake City?

Radius of earth is 6,371 kmSLC is at 40.75 degrees North latitude

What is magnitude of centripetal acceleration?

Mechanics Lecture 3, Slide 28

v(t1) = v

1

v(t2) = v

2

Note that angle between v2 and

v1 is just !

So, a = dv/dt = vd/dt = v = v2/R

Mechanics Lecture 3, Slide 29

We can ignore acceleration due to Earth's rotation since it's small

Example: What would be radius of a sphere, with the same linear speed on its equator as the Earth, for which an object on its surface would experience a centripetal acceleration of g = 9.81 m/s2?

Mechanics Lecture 3, Slide 31

Prelecture Slide: Discuss