Mechanics Lecture 3, Slide 1

Physics 2111

Unit 3

Unit Concepts:a) Circular Motion

b) Relative motion

Where are we?

Mechanics Lecture 3, Slide 2

Mechanics Lecture 3, Slide 3

DQ = DS/R w is the rate at which the angle q changes:

q

d

dt

qw

Circular Motion

Another example of 2D motion….let’s

define some things…..

Unit 3, Slide 4

dv R

dt

q

dq

v dt

R

=R dq

Another way to see it:

v = wR

v = Rw

Once around:

w Dq / Dt = 2p / T

v Dx / Dt = 2pR / T

Circular Motion

Mechanics Lecture 3, Slide 5

Centripetal Acceleration

Mechanics Lecture 3, Slide 6

Example 3.1 (Going around corner)

200m

If you went around a curve

with a radius of 200m at a

constant velocity of 15m/sec,

what would the magnitude of

your acceleration be?

What if your velocity were

30m/sec?

What is the radius were 100m?

Mechanics Lecture 3, Slide 7

Example 3.2 (Merri-go-round)

What is the magnitude of your

acceleration if you’re on a merri-go-round

with a radius of 5m that goes around once

every minute?

Mechanics Lecture 3, Slide 8

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

Mechanics Lecture 3, Slide 9

ac ab bcv v v What you just did

Relative Motion

What is the

velocity of Mike

with respect to

the ground?

Mechanics Lecture 3, Slide 10

Prelecture 3, Question 1

Mechanics Lecture 3, Slide 11

Checkpoint

A girl stands on a moving sidewalk that moves to the right at 2 m/s relative to the ground. A dog runs toward the girl in the opposite direction along the sidewalk at a speed of 8 m/s relative to the sidewalk.

What is the magnitude of 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

Mechanics Lecture 3, Slide 12

vbelt,ground = 2 m/s

vdog,belt = 8 m/s

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

Checkpoint

A girl stands on a moving sidewalk that moves to the right at 2 m/srelative to the ground. A dog runs toward the girl in the opposite direction along the sidewalk at a speed of 8 m/s relative to the sidewalk.

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

Mechanics Lecture 3, Slide 13

Example 3.3 (Hungry Bat)

What is the velocity of the insect with respect to the

bat?

A hungry bat detects lunch: an insect buzzing around.

The velocities of the bat and of the insect with respect to

the ground are shown.

30o

50o

4m/sec

5 m/sec

Unit 3, Slide 14

Racheal can swim at 2.1 m/sec with respect to the water. If she wants to swim across a river that is 10 meters wide and flows at 1.2m/sec.

If she attempts to swim straight across, how long will it take her?

Where will she be when she reaches the other side?

1.2m/sec

Unit 3, Slide 15

Now let’s say Racheal wants to wind up direction across from where she started.

At what angle should she swim?

How long does it take her to reach the other side?

1.2m/sec

Mechanics Lecture 3, Slide 16

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, Annswims 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

Question

Mechanics Lecture 3, Slide 17

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