
What are the three types of motion?

There is a special point in a system or object called the ______ ____ _____, that moves as if all the mass of the system is concentrated at that point. The system will move as if an external force were applied to a _______ ______ of mass M (where will this be located?)
 center of mass
 single particle
 center of mass

For a simple object such as a sphere, block, or cylinder, whose density is constant (homogeneous), the center of mass is at the _______ _______. Where does the center of mass tend to be for irregular or complicated objects?
 geometric center
 Tends to lie closer to the heavier objects or particles that make up the entire object

What is the formula for the center of mass for both x and y coordinates

Gravity doesn't act at a single point on an object, it pulls downward on _____ _____ that makes up the object. However, the gravitational force can be calculated by assuming that the _____ _____ of gravity acts at a single special point on the object called its ______ _____ _____
 every particle
 net force
 center of gravity

Any object free to rotate about a pivot will come to rest with its center of gravity directly ______ the pivot. Define the center of gravity
 directly below
 Center of gravity: the average position of the gravitational forces on all parts of the object

What is the difference between center of gravity and center of mass?
 Center of mass determines trajectory of objects, the object will move as if all of its mass was concentrated at that point.
 Center of gravity determines downward pull of gravitational force, gravity will act on every particle on the object and this will be most apparent where the object has the highest concentration of particles




Uniform circular motion occurs when an object moves in a _____ path with a _____ speed, v. If speed is constant, what about acceleration?
 circular
 constant
 Speed is constant = magnitude of velocity is constant, but direction of velocity is different at any time so acceleration is never zero, a ≠ 0
 *This change in velocity is related to an acceleration

The velocity vector is always ______ to the path of the object and the velocity is ______ to the radius of the circular path
 tangent
 perpendicular

The period, T, is the time interval required for one complete revolution. What is the formula for both speed and period in this context
 speed = perimeter/period
 T = 2πr/v

A rigid object is one that is _________. The relative locations of all particles making up the object remain ______. When a rigid body is rotating about a fixed axis, every particle on the object rotates about that axis through three factors that remain the same (name them)
 nondeformable
 constant
 same angular displacement, angular speed and angular acceleration

Polar coordinates are convenient to use to represent the position of P (or any other point). P is located at (__,__)
 (r,θ)
 *θ is measured counterclockwise from the reference line

Define angular position (state the S.I. unit and how to convert from degrees to radians)
 Angular position: the angular position of the rigid object is the angle between the reference line on the object and the fixed reference line in space

As the particle moves in uniform circular motion, the only coordinate that changes is θ. As the particle moves through θ, it moves through an arc length s = ____ and Δθ = _____
 s = rΔθ
 Δθ = θf  θi

State the formula for average angular velocity of a particle

For a particle moving with uniform circular motion, ω is ______. Define angular speed and state the units
 constant
 Angular speed: absolute value of the angular velocity (scalar quantity, no direction)
 S.I. Units: rad/s or s^{1} (since radians have no dimensions)
 *also measured in rev/s and rpm

What are the rules for knowing if angular velocity will be < or > 0?

Since particles move in a circular motion, translational velocity is always _____ to the path (_____ velocity)
s (_____ ____) = ___
What is the formula for tangential aka linear velocity
 tangent
 (tangential velocity)

 B. Angular velocity/speed is the same between a and b
 *Don't mix up with linear velocity/speed

The acceleration is always _______ to the path of motion. It always points to the _______ of the circle of motion. This acceleration is called the _______ ________
 perpendicular
 center
 centripetal acceleration

What is the formula/magnitude of the centripetal acceleration vector?
What is its direction?

Angular acceleration α measures how rapidly the ______ ______ is changing:
What is the formula for average angular acceleration, α_{avg}:
 angular velocity

State the formula and units for instantaneous angular acceleration, α:

When is angular acceleration positive and when is it negative?

Consider a particle moving to the right along a curved path where the velocity changes both in direction and in magnitude. In this case, there would be both _______ _______ and _______ _______
 centripetal acceleration and tangential acceleration

What is the formula for:
Total acceleration
Tangential acceleration
Radial acceleration
*which direction does each unit vector point?



All points on the rigid object will have the same ______ speed, but not the same _______ speed. All points on the rigid object will have the same ________ acceleration, but not the same ________ acceleration. The tangential quantities depend on the _______ which is not the same for all points on the object
 angular speed
 tangential speed
 angular acceleration
 tangential acceleration
 radius

State the 4 rigid body (constant angular acceleration) formulas
*Bonus: state the 4 particle under constant acceleration formulas

State the formula for:
1) Angular displacement at constant angular speed
2) Change in angular velocity at constant angular acceleration
*Bonus: state the equivalent linear motion formulas
 1) Δθ = ωΔt  Δx = vΔt
 2) Δω =αΔt  Δv = αΔt

What is the formula for:
angular position
angular velocity
tangential acceleration
 θ = s/r (*s = arc length)
 ω = v/r (*v = tangential speed)
 a_{t} = αr


A particle of mass m moving at constant speed v around a circle of radius r must have an acceleration, a_{c} = ___ = ___ pointing toward the ______ of the circle
 a_{c} = v^{2}/r = rω^{2}
 center

The net force associated with the centripetal acceleration is the centripetal force. This force is a _____ force, not a physical force. Newton's second law along the radial direction gives?
 net force

This centripetal force causes a change in the direction of the ______ ______. If the force vanishes, the object would move in a straightline path ______ to the circle

Strategy for solving Circular Dynamics Problems: (6story)

What are the 5 typical cases in Circular Dynamics
 Horizontal circular motion with a string
 Unbanked curve motion
 Banked curve motion
 Looptheloop: vertical circular motion without tied to a string
 Vertical circular motion with a string

Explain the horizontal circular motion with a string:
A mass is tied to a cord or string which generates _______ force. Only that force is along the _______ direction (state the newton's 2nd law).
What can be said about this force reaching its maximum limit?
 Tension force
 radial direction
 ΣF_{r} = T = ma_{c} = mv^{2}/r
 Once T > maximum limit:
 1) The cord or string will break.
 2) No more circular motion
 3) v = v_{tang} = constant, a straight line path

Explain Unbanked curve motion (car)
______ friction prevents a car from skidding radially outward when turning an unbanked curve.
State Newton's second law
 Static friction
 ΣF_{r} = f_{s} = ma_{c} = mv^{2}/r
 *Keep in mind this is the upper limit of static friction so you'll be asked to find the maximum speed limit

Explain Banked curve motion (car):
If the path is nearly negligible, then can you can't use ______ force to make the the turn. Instead, the _____ force prevents the car from skidding. State Newton's 2nd Law
The _____ of the banked curve determines the maximum speed
 friction force
 Normal force
 ΣF_{r} = N_{r} = mv^{2}/r
 angle

Explain the Looptheloop: Vertical circular motion without being tied to a string:
The ______ (state the min possible value) and component of ________ force are along the radial direction, depends on the location of the object in the loop. State Newton's 2nd law
 normal force (N ≥ 0)
 gravitation force


Explain vertical circular motion with a string:
Similar to the looptheloop, but involve ______ instead of ______ force. State Newton's 2nd law
Which force has an upper breaking limit?
 Tension and not normal force

What is the max walking speed formula?

A force that seems to push an object to the outside of a circle is called a ________ force. E.g. When you're making a turn, you feel there is a force pushing your body outward. However, your body is just trying to move forward in a straight line while the car is making a turn. So what can be said of this outward force?
 centrifugal force
 It doesn't exist

Provide free body diagram and newton's 2nd law for riding a Ferris wheel (at the top and at the bottom)




 Centripetal acceleration: They are all the same because speed is constant and there is no change in radius
 Normal force: A = E > B = D > C
 Apparent weight: A = E > B = D > C

