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List what each variable (alpha, theta, omega) represent in rotation.

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How does each rotational variable (alpha, theta, omega) relate back to linear variables?

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theta: radians of rotation
omega: angular velocity

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alpha is angular rotation
theta is angular displacement
omega is angular velocity

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Omega= Angular Velocity
Alpha= Angular Acceleration
Theta= Angular Displacement

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Alpha is angular rotation
Theta is the angle degrees
Omega is the angular velocity

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alpha angular acceleration
theta angle/degrees
omega angular velocity

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alpha: angular acceleration
theta: angular position
omega: angular velocity

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Theta: angular position
Omega: angular velocity
Alpha: angular acceleration

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alpha: angular acceleration
omega:angular velocity
theta: angular position

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Alpha: angular acceleration
Theta: angular displacement
Omega: angular velocity

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Theta:angular postion
Alpha:  angular acceleration
Omega: angular velocity

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theta: position, x
omega: velocity, v

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Alpha: angular rotation
Theta: angular position
Omega: angular velocity

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position is the same(where it is)
velocity is a derivative of position
acceleration is a derivative of velocity

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From Example 1, Use the results in parts a-c to describe the motion of the disk from t=-3s to t=6s

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Theta: Position (x)
Omega: velocity (v)
Alpha: acceleration (a)

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Alpha: angular acceleration
Theta: angular position
Omega: angular velocity

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theta: position (x)
omega: velocity(v)- derivative of position
alpha: acceleration(a)- derivative of velocity

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X, V, A are all related in the same sense, without the rotation

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alpha=acceleration
omega=velocity
theta=distance

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theta: x, position
alpha: a, acceleration
omega: v, velocity

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Theta= postion(x)
Omega= velocity(v)
alpha=acceleration (a)

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Theta: x, position
Omega: v, velocity
Alpha: a, acceleration

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Alpha: angular acceleration
Theta: angular position
Omega: angular velocity

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Theta: x position
Omega: v velocity
Alpha: a acceleration

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Alpha angular rotation
Theta angular position
Omega angular  velocity

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before time 1.2 it is rotating counterclockwise and after 1.2 it is rotating clockwise

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Starting at 3 seconds the postion is about 3.05 and the disk is turning clockwise. The velocity is becoming more postive and at t=1.2 the velocity is zero. After t=1.2 the velocity is postive and increasing and the disk is spinning counterclockwise. At t=6 it will have a velocity of 2.4 radians/s and the postion wll be 4.4 rad.

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Alpha acceleration
Theta position
Omega velocity

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the disk turns clockwise from -3 to 1.2 sec and turns counterclockwise after 1.2 to 6 sec

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it's spinning clockwise until x=0 then it starts going the opposite way

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its rotating counter clockwise until 1.2 sec, then starts turning clockwise

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Before 1.2 seconds the disk is rotating counter clockwise but after the 1.2 seconds the disk begins to rotate clockwise.

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The disk is rotating counter clockwise before 1.2 seconds and begins to rotate clockwise after

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The disk rotates counter clockwise, after 1.2 seconds it begins to rotate clockwise.

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Work shown on Jamboard

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a.32 seconds
b.At t=0 the velocity of the grindstone is negative so it is spinning clockwise. After 13.1 seconds the velocity is zero, so the grindstone momentarily stops and then starts spinning countercockwise and since it has a postive accleration, the velocity is increasing as time apporaches 32 seconds at which point the grind stoone has done 5 revs (10pi rads)
c. 13.1 seconds

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a. 32 seconds
b.
c. 13.1 seconds

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A. 32 seconds
B. The grindstone is spinning clockwise at T=0. After 13.1 seconds the grindstone reaches a velocity of ), and then rotates again in a counterclockwise direction.
C. 13.1 seconds

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A) 32 seconds
B)
C) 13.14s

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a) 31.9s
b)
c) 13.1s

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Newton's 2nd Law

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-1.094Nm

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-1.95 Nm

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-3.85 N m

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Force is directly proportional to mass and acceleration.
F=ma

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Net force equals to the mass and acceleration

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Force is dependent to mass and acceleration.

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F=ma

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the greater the mass, the more force required to move that object
F=ma

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F=ma

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f=ma

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2 Js

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2km/s

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0.688 rev/s : wb
spinning counter clockwise

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ccw

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ccw

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0.688 rev/s CCW

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0.96 rads/s