Transcript Power point review

Pg. 123-125; Chapter 11

Circular Motion- Object spins around an
external axis


Ex. KD-4 Lab, horses on a carousel, swinging bat
Rotational Motion-Object spins around its
own center of gravity (it’s own internal axis)

Ex. bicycle wheel, earth, globe, carousel, wind mill,
somersault

Center of mass/gravity-The average position
of weight distribution

To find center of gravity: balance an object
Linear
Rotational/Angular
Displacement (d)
Angular Displacement (Θ)
Units: (m, km, cm)
Units: (degrees, revolutions,
radians)
1 m = .001 km=100 cm
360°=1 rev=2л radians
d
Linear
Rotational/Angular
Velocity (v)
Angular velocity– (ω)
Unit: (m/s)
Unit: (rev/s, rad/s)
Formula: v =∆d/∆t
Formula: ω=∆Θ/∆t
-need to convert to rad/s
using formulas
Linear
Rotational/Angular
Acceleration (a)
Angular Acceleration (a)
Unit: (m/s²)
Units: (rev/s², rad/s²)
Formula: a=∆v/∆t
Formula: a=∆ω/∆t
Linear
Rotational/Angular
Inertia”Laziness”
Rotational Inertia (I) –Resistance to rotation
“Laziness” of a rotating thing
Depends on Depends on mass AND where the mass is!!!
mass (m)kg
Unit: kgm²
Formulas:
Thin ring: I=mr²
Solid sphere: I= 2/5 mr²
Solid disk: I = ½ mr²

What is the rotational inertia of a .50 kg
basketball with a radius of .15 m?

Inertia for a hollow sphere I = 2/3 m r2

I = 2/3 (.50kg) (.15m)2

I = .0075 kg m2

Depends on the mass and how the mass is
distributed

Mass on outside (away from center of rotation) =
high rotational inertia (more “laziness”)
 Ex) Hollow sphere

Mass close to center of rotation = low rotational
inertia (less inertia)
 Ex) Solid disk


Increase rotational inertia by increasing the
distance between the bulk of the mass and axis of
rotation (Ex: tight-rope walker)
Decrease rotational inertia by decreasing the
distance of the mass to the center axis (choke up on
bat, bend legs when run)
Linear
Rotational/angular
Force (F)
Torque ()
Unit: Newton (N)
Formula:  = F x r
Unit: Nm
Formula: F = m a
Formula:  = I a
F x r= I a


1. Apply force perpendicular to lever arm
2. Increase length of lever arm
Linear
Rotational/Angular
Kinetic Energy (K.E)
Kinetic Energy (K.E.)
Unit: Joule (J)
Unit: J
Formula: K.E. = ½ m v²
Formula: K.E. = ½ I ω²
Work (W)
Work (W)
Unit: Joule (J)
Unit: J
Formula: W = Fd
Formula: W = Torque Θ
Momentum (p)
Angular Momentum (L)
Unit: kgm/s
Unit: kgm²/s
Formula: p = mv
Formula: L = Iω

Conservation of Angular Momentum-Angular
momentum remains constant during rotation
unless an outside force acts on it

Rotational inertia can be changed “in midflight” by rearranging mass

Precession- The motion resulting from the
sum of 2 angular velocities


Caused by a torque
Ex. bicycle rider, a top, gyroscope