The best way to understand how tangential velocity and tangential acceleration are related is to visualize from above. Will you look at that! This video does exactly that.

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Content Times:

0:10 Visualizing up the three parts of the demonstration

0:51 Visualizing the tangential velocities

1:41 Visualizing the tangential accelerations

3:11 Visualizing tangential velocities and accelerations simultaneously

4:52 Angular vs. Tangential quantities

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Tangential Acceleration is introduced and visualized. Example problem is worked through. We even relate arc length, tangential velocity, and tangential acceleration via the derivative! Example: A record player is plugged in and uniformly accelerates to 45 revolutions per minute in 0.85 seconds. Mints are located 3.0 cm, 8.0 cm, and 13.0 cm from the center of the record. What is the magnitude of the tangential acceleration of each mint?

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Content Times:

0:21 The tangential acceleration equation

0:55 Translating the example problem

2:13 Solving for angular acceleration

3:02 Solving for tangential accelerations

4:16 Visualizing the tangential accelerations

5:05 Using the derivative to relate arc length, tangential velocity, and tangential acceleration

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]]>Three mints are sitting 3.0 cm, 8.0 cm, and 13.0 cm from the center of a record player that is spinning at 45 revolutions per minute. What are the tangential velocities of each mint?

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Content Times:

0:08 Translating the problem

1:11 Solving the problem

2:12 Visualizing the tangential velocities

2:42 The direction of tangential velocity

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Humans are best for demonstrating Tangential Velocity and understanding that it is not the same as angular velocity.

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Content Times:

0:10 Beginning the demonstration

1:19 Adding the last human

1:50 What was different for each human?

2:44 Visualizing tangential velocity using an aerial view

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What is the angular acceleration of a compact disc that turns through 3.25 revolutions while it uniformly slows to a stop in 2.27 seconds?

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Content Times:

0:08 Translating the problem

0:52 Determining which Uniformly Angularly Accelerated Motion (UαM) equation to use

1:54 Using a second UαM equation

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]]>Using Uniformly Accelerated Motion (UAM) as a framework to learn about Uniformly Angularly Accelerated Motion (UαM). Just like UAM, UαM has 5 variables, 4 equations and if you know 3 of the UαM variables, you can determine the other 2 UαM variables, which leaves you with 1 …

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Content Times:

0:15 Introducing Uniformly Angularly Accelerated Motion! (UαM)

0:38 Reviewing Uniformly Accelerated Motion

1:22 When can we use the UαM Equations?

2:24 The four UαM Equations

4:20 Examples of objects in UαM

4:48 Average and instantaneous angular velocity and the UαM equations

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A record player is plugged in, uniformly accelerates to 45 revolutions per minute, and then is unplugged. The record player (a) takes 0.85 seconds to get up to speed, (b) spends 3.37 seconds at 45 rpms, and then (c) takes 2.32 seconds to slow down to a stop. What is the average angular acceleration of the record player during all three parts?

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Content Times:

0:08 Translating the problem

2:35 Solving part (a) - angular acceleration while speeding up

3:13 Solving part (b) - angular acceleration at a constant angular velocity

3:57 Solving part (c) - angular acceleration while slowing down

4:36 Reflecting on all 3 parts simultaneously

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Angular acceleration is introduced by way of linear acceleration. The units of radians per second squared are discussed. Examples of objects which angular acceleration are shown.

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Content Times:

0:23 Average angular acceleration

1:02 Angular acceleration units

1:37 Demonstrating objects which have angular acceleration

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The wheel of a bike rotates exactly 3 times in 12.2 seconds. What is the average angular velocity of the wheel in (a) radians per second and (b) revolutions per minute?

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Content Times:

0:08 Translating the problem

1:32 Solving for the angular velocity in radians per second

2:22 Converting from radians per second to revolutions per minute

3:24 Three common mistakes made by students when doing this conversion.

4:37 Alternate and easier solution for part b

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The equation for average angular velocity is presented in relation to the equation for average linear velocity. Radians per second and revolutions per minute are discusses as the units for angular velocity. Objects which have angular velocity are shows.

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Content Times:

0:09 Average linear velocity

0:22 Average angular velocity

0:53 The units for angular velocity

1:37 Examples of objects with angular velocity

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