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Pipeng : Physics Cyclical Motion : Angular Velocity Displacement And Acceleration BETA Physics Homework Module

Angular Velocity BETA Physics Module

Description : Physics cyclic motion homework exercises : rotational motion

Tools In This Module:

BETA : Cyclic : Rotational Motion 01 : Rotational Motion versus Linear Motion : BETA Physics Homework Exercise
BETA : Cyclic : Rotational Motion 02 : Average Rotational Speed From Rotation (Angle) And Time : BETA Physics Homework Exercise
BETA : Cyclic : Rotational Motion 03 : Final Rotational Velocity From Initial Velocity Acceleration And Time : BETA Physics Homework Exercise
BETA : Cyclic : Rotational Motion 04 : Rotation (Angle) From Initial Velocity Acceleration And Time : BETA Physics Homework Exercise
BETA : Cyclic : Rotational Motion 05 : Rotation (Angle) From Initial Velocity Final Velocity And Time : BETA Physics Homework Exercise
BETA : Cyclic : Rotational Motion 06 : Final Rotational Velocity From Initial Velocity Acceleration And Rotation : BETA Physics Homework Exercise
BETA : Cyclic : Rotational Motion 07 : Rotational Velocity Frequency RPM Period And Instantaneouis Velocity : BETA Physics Homework Exercise


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Module List

BETA : Cyclic : Rotational Motion 01 : Rotational Motion versus Linear Motion : BETA Physics Homework Exercise

Description : Rotational motion versus linear motion.

Discussion : The linear motion of any point is proportional to the rotaional motion times the radius. See Figure Rotational Motion versus Linear Motion

The homework exercise has 3 sets of questions with 3 questions per set.

d, v and a
r, omega and alpha
r, d and alpha

There are 3 questions per homework exercise :

d = theta r
v = omega r
a = alpha r

rearranging

r = d / theta = v / omega = a / alpha
theta = d / r
omega = v / r
alpha = a / r

where

d = linear displacement
v = linear velocity
a = linear acceleration
r = radius
theta = rotation angle (θ)
omega = rotational velocity (ω)
alpha = rotational acceleration (α)

By convention rotational or angular vectors are orientated along the axis of rotation.

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BETA : Cyclic : Rotational Motion 02 : Average Rotational Speed From Rotation (Angle) And Time : BETA Physics Homework Exercise

Description : Average rotational velocity amplitude from rotation angle and time.

Discussion : Rotational velocity amplitude (or speed) is the scalar value of the rotational velocity vector. See Figure Rotational Motion versus Linear Motion

The homework exercise has 3 sets of questions with 2 questions per set.

omegaa, theta
theta, omegaf
t, omegai

The basic equations are :

omegaa = (omegai + omegaf) / 2
theta = omega t

rearranging

alpha = 2 * (omegaf - omegaa) / t
omegaf = omegai + alpha * t
t = theta / omegaa
omegaa = theta / t

where

omegai = initial velocity (ωa)
omegaf = final velocity (ωf)
omegaa = average velocity (ωa)
theta = rotation angle (θ)
t = elapsed time
alpha = rotational acceleration (α)

By convention rotational or angular vectors are orientated along the axis of rotation.

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BETA : Cyclic : Rotational Motion 03 : Final Rotational Velocity From Initial Velocity Acceleration And Time : BETA Physics Homework Exercise

Description : Final rotational velocity amplitude from the initial rotational velocity amplitude, rotational acceleration and time.

Discussion : Rotational velocity amplitude (or speed) is the scalar value of the rotational velocity vector. See Figure Rotational Motion versus Linear Motion

The homework exercise has 4 sets of questions with 3 questions per set.

omegaf, omegaa, theta
t, theta, omegaa
alpha, omegaa, theta
omegai, theta, omegaa

The basic equations are :

omegaf = omegai + alpha t
omegaa = (omegai + omegaf) / 2
theta = omegaa t

rearranging

omegai = omegaf - alpha t
alpha = (omegaf - omegai) / t
t = (omegaf - omegai) / alpha

other equations

omegaa = (omegai + omegaf) / 2
theta = (omegai + omegaf) t / 2
omegaa = theta / t

where

omegai = initial velocity (ωa)
omegaf = final velocity (ωf)
omegaa = average velocity (ωa)
theta = rotation angle (θ)
t = elapsed time
alpha = rotational acceleration (α)

By convention rotational or angular vectors are orientated along the axis of rotation.

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BETA : Cyclic : Rotational Motion 04 : Rotation (Angle) From Initial Velocity Acceleration And Time : BETA Physics Homework Exercise

Description : Rotation angle from the initial rotational velocity amplitude, rotational acceleration and time.

Discussion : Rotational velocity amplitude (or speed) is the scalar value of the rotational velocity vector. See Figure Rotational Motion versus Linear Motion

The homework exercise has 4 sets of questions with 3 questions per set.

theta, omegaa, omegaf
omegaa, omegai, omegaf
omegaa, omegaf, alpha
omegaf, omegaa, t

The basic equations are :

theta = omegai t + 0.5 alpha t2
omegaf = omegai + alpha t
omegaa = theta / t

other equations

omegaa = (omegai + omegaf) / 2
omegaf = omegai + alpha * t
omegaa = theta / t
omegaf2 = omegai2 + 2 * alpha * d

where

omegai = initial velocity (ωa)
omegaf = final velocity (ωf)
omegaa = average velocity (ωa)
theta = rotation angle (θ)
t = elapsed time
alpha = rotational acceleration (α)

By convention rotational or angular vectors are orientated along the axis of rotation.

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BETA : Cyclic : Rotational Motion 05 : Rotation (Angle) From Initial Velocity Final Velocity And Time : BETA Physics Homework Exercise

Description : Rotation angle from the initial rotational velocity amplitude, final rotational velocity amplitude and time.

Discussion : Rotational velocity amplitude (or speed) is the scalar value of the rotational velocity vector. See Figure Rotational Motion versus Linear Motion

The homework exercise has 4 sets of questions, with three questions per set.

theta, omegaa, alpha
omegai, omegaa, alpha
omegaf, omegaa, alpha
t, omegaa, alpha

The basic equations are :

theta = (omegai + omegaf) t / 2
omegaa = theta / t = (omegai + omegaf) / 2
alpha = (omegaf - omegai) / t

rearranging

omegai = 2 theta / t - omegaf
omegaf = 2 theta / t - omegai
t = 2 theta / (omegaf - omegai)

other equations

omegaa = (omegai + omegaf) / 2
alpha = (omegaf - omegai) / t
omegaa = theta / t

where

omegai = initial velocity (ωa)
omegaf = final velocity (ωf)
omegaa = average velocity (ωa)
theta = rotation angle (θ)
t = elapsed time
alpha = rotational acceleration (α)

By convention rotational or angular vectors are orientated along the axis of rotation.

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BETA : Cyclic : Rotational Motion 06 : Final Rotational Velocity From Initial Velocity Acceleration And Rotation : BETA Physics Homework Exercise

Description : Final rotational velocity amplitude from the initial rotational velocity amplitude, rotational acceleration amplitude and and rotation angle.

Discussion : Rotational velocity amplitude (or speed) is the scalar value of the rotational velocity vector. See Figure Rotational Motion versus Linear Motion

The homework exercise has 4 sets of questions with 3 questions per set.

omegaf, omegaa, t
omegaf, alpha, theta
alpa, omegaa, t
theta, t, omegaa

The basic equations are :

omegaf2 = omegai2 + 2 alpha theta
omegaa = theta / t = (omegai + omegaf) / 2
alpha = (omegaf - omegai) / t

rearranging

omegai2 = omegaf2 - 2 * alpha * d
alpha = (omegaf2 - omegai2) / (2 * d)
d = (omegaf2 - omegai2) / (2 * a)

other equations

omegaa = (omegai + omegaf) / 2
t = (omegaf - omegai) / alpha
omegaa = d / t

where

omegai = initial velocity (ωa)
omegaf = final velocity (ωf)
omegaa = average velocity (ωa)
theta = rotation angle (θ)
t = elapsed time
alpha = rotational acceleration (α)

By convention rotational or angular vectors are orientated along the axis of rotation.

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BETA : Cyclic : Rotational Motion 07 : Rotational Velocity Frequency RPM Period And Instantaneouis Velocity : BETA Physics Homework Exercise

Description : Convert between rotational velocity, frequency, rpm, period and instantaneous velocity.

Discussion : There are several methods to describe rotational velocity. Frequency is the number of cycles or revolutions per second. RPM is the number of cycles or revolutions per minute. The period is the time to complete one cycle or revolution. The instantaneous velocity is the linear velocity of a point on the radius. See Figure Rotational Motion versus Linear Motion

The homework exercise has 4 sets of questions with 4 questions per set.

v, f, T, rpm
omega, r, T, rpm
rpm, f, omega, v
T, f, omega, r

The basic equations are :

v = omega r
f = omega / (2 π)
T= 2 π / omega
rpm = 30 omega / π

rearranging

omega = 2 π f
T = 1 / f
f = 1 / T
rpm = 60 f
f = rpm / 60

where

omega = rotation velocity (ω)
r = radius
v = instantaneous linear velocity
f = frequency
rpm = revolutions per minute
T = period

π is the javascript symbol for pi (π).

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