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the angular position
What is the most basic angular quantity?
What is a reference line?
a spot that is analogous to the origin in a linear coordinate system
Suppose there is a spot on a tire. What is the angular position of the spot?
the angle θ that a line from the axle to the spot makes with a reference line
radians (which are dimensionless)
What are the units of θ?
When is θ positive?
When counterclockwise rotation from the reference line occurs
When is θ negative?
When clockwise rotation from the reference line occurs
Linear distance around a circle
What is a radian?
-the angle for which the arc length on a circle of radius r is equal to the radius of the circle
s = rθ
What is the relationship between arc length, radius, and θ?
the circumference of a circle
In one complete revolution, what is the arc length?
C = 2πr
What is the circumference of the circle equal to?
displayed as the change in theta (∆θ)
What is it equal to?
Δθ = θ final - θ initial
average angular velocity
What is ω average?
What is this analogous to?
the definition of average linear velocity
When rotation is counterclockwise
When is ω > 0?
When rotation is clockwise
When is ω < 0?
In addition to angular velocity, what is the symbol ω also used for?
What is a period?
the time to complete one revolution
T = 2π/ω
What is T equal to?
represented by a lower case alpha (α)
What is α equal to?
α = Δω / Δt
angular speed increases in the positive direction
If α is greater than zero, and ω is greater than zero, what is the effect on angular speed?
angular speed increases in the negative direction
If α is les than zero, and ω is les than zero, what is the effect on angular speed?
-angular speed will decrease, then will increase in the positive direction
If α is greater than zero, and ω is less than zero, what is the effect on angular speed?
-angular speed will decrease, then will increase in the negative direction
If α is les than zero, and ω is greater than zero, what is the effect on angular speed?
the linear velocity of an object
In words, what is the tangential velocity of a rotating object?
tangential velocity = rω
Using an equation, describe the tangential velocity of an object
radians per second
What is angular velocity measured in
the units of the magnitude of a vector could be _(3 examples)depending on which particular _
What is it denoted by?
s = rΔθ
What is the relationship between s and θ?
the arc-length formula
What is this formula called?
2pi x r
C = r(2π)
What is circumference equal to?
What is 2π equal to?
the distance around a circle in radians
When an object moves in the positive direction, is it moving cw or ccw?
When an object moves in the negative direction, is it moving cw or ccw?
What is 90 degrees equal to in radians?
What is 180 degrees equal to in radians?
What is 360 degrees equal to in radians?
If angular displacement remains the same, what is the effect on s if r is increased?
yes they do
Given two people on a carousel ride, one is closer to the center of the circle than the other. Do persons A and P take their trip in the same period of time?
Can total system momentum still be conserved if it is not an isolated system?
the person on the outside of the circle has a greater linear velocity than the person on the inside of the circle
Does ionic bonding occur between elements with very different electronegativities?
because both person a and B cover the same angle in the same time
using: v tangential = rω
object speeds up
When an object moves in a circle, if ω and α are in the same direction, what happens to its speed?
object slows down
if ω and α are in the opposite direction, what happens to its speed?
A force directed towards the center of a circle that causes an object to follow a circular path
a = centripetal acceleration
What is it responsible for?
changing the direction of an object as it moves in a circle
To summarize, what effect do internal forces have on the net momentum of a system?
What type of acceleration does the tangential force produce?
to Change speed
What is its role?
the object speeds up
When linear velocity and tangential acceleration are in the same direction, what happens to the speed of the object?
ω is positive
Describe ω in this instance
the speed of the object is increasing
-the angle between the velocity and the acceleration total will be less than 90 degrees
What will be the possible range of values for the angle between the velocity and acceleration total?
the speed of the object decreases
When linear velocity and a tan are in opposite directions, what happens to the speed of the object?
α is negative
Describe α in this instance
-the angle between the velocity and the total acceleration will be greater than 90 degrees
What will be the possible range of values for the angle between the velocity and the total acceleration?
the speed of the object remains constant
When a tan equals zero, what happens to the speed of the object
Describe α in this instance
α is equal to zero
In what direction does Fnet always point?
always in the same direction as acceleration
both are tasked with describing speed changes
Describe the relationship between a tan and α?
a tan = rα
What equation is used to describe the relationship between a tan and α?
a centripetal = rω^2
What is the relationship between centripetal acceleration, r, and ω?
a tangential = rα
What is the relationship between tangential acceleration, r, and ω?
a changing tangential speed
What is acceleration tangential caused by?
a changing direction of motion
What is acceleration centripetal caused by?
the vector sum of the two
In cases where both centripetal and tangential accelerations are present, what is total acceleration equal to?
using the pythagorean theorem
Since centripetal and tangential acceleration will always be at right angles to each other, how is the magnitude of the total acceleration calculated?
using Inverse tan
How is the direction of the total acceleration calculated?
all points on the rigid object have the same angular speed
A rigid object rotates around a fixed axis. Do all points on the object have the same angular speed? Do all points on the object have the same linear speed? Explain
-no, because the direction of motion is constantly changing
At the local carnival, you take a ride on the Ferris wheel. While on the Ferris wheel, is your linear velocity constant?
yes it is
Is your linear speed constant?
a basketball thrown with no spin
Give an example of an object that has zero rotational kinetic energy but nonzero translational (linear) KE
a spinning airplane propeller on a plane that is at rest
Give an example of an object that has zero translational (linear) KE but nonzero rotational KE
a bicycle wheel on a moving bicycle
Give an example of an object that has nonzero rotational and translational KEs
-in the time t/2, the object rotates through the angle of θ/4.
An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θ in the time t, through what angle did it rotate in the time t/2?
equal to the rotational period of Betsy
Two children ride on the same merry-go-round. Jason is distance R from the axis of rotation; Betsy is a distance 2R from the axis. Is the rotational period of Jason greater than, less than…
if take off and landing heights of a trajectory of a projectile are the same, then the time from ground to apex should be _______ the time from apex to ground
the linear speed of Bob is greater than that of Abe
Abe and Bob both stand on a rotating carousel. Abe is halfway out to the edge, while Bob rides on the very edge. Compare the linear speed of Bob to that of Abe.
Compare the angular speed of Bob to that of Abe
the angular speed of Bob is equal to that of Abe
What are tangential accelerations provided by?