Monday, November 3

Review for Exam IIIChapters 6, 7, 8(springs only) 9

Acceleration2

c

v

r Centripetal

ta r tangential

sinr F rF r F

Torque = τ

Center of Mass

Net torque of gravitational forces is zero about center of mass

ii

iii

CM m

xmx

2ii

I m rMoment of Inertia and Newton’s 2nd law

I F ma

• Center of Gravity (center of mass)

• Moment of Inertia

• Torque

ii

iii

CM m

xmx

2 2 2 21 1 2 2 3 3 .... ii

I m r m r m r m r

sinI rF

Hooke’s Law

spF k x

Momentum

f i

p mv

J p p p

Conservation of Momentum

When is momentum conserved?

i fP P

Special Case: Perfectly Inelastic Collision

1 2

1 1 2 2 1 2

objects stick together

m

xf xf xf

xi xi xf

v v v

v m v m m v

Which has the greater moment of inertia?

Example

• How long does it take the small mass to fall 1.0 m when released from rest?

1.2m

M1 = 35 kg M2=20kg

x = ?

Find x

• The spring’s equilibrium length is 30 cm. The mass of the fish is 4.0 kg, and causes the spring to stretch to a length of 42 cm.– What is the spring constant of the spring?– If an 8.0 kg fish is suspended, what will be the length of the

stretched spring?

Example: (pg. 282 in book)