16. Rotational Mechanics Basics, Radians & Angular Velocity

Question 1

Normally we measure angles in a unit called…

Answer 1

Radian

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Question 2

Define Radians

Answer 2

One radian is an angle where the radius is equal to the arc length.

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Question 3

1 rotation = ?

Answer 3

2π rad

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Question 4

360° = ?

Answer 4

2π rad

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Question 5

How do you convert an angle to radians?

Answer 5

160°/1 • 2π rad/360° = 2.79 rad

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Question 6

How to convert radians to rotation?

Answer 6

2.79 rad/1 • 1 rot/2π rad = 2.79/2π = 0.444 rotation

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Question 7

What does rpm stands for?

Answer 7

Rotation per minute

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Question 8

How do you convert 300RPM to Rad/s?

Answer 8

300rot/1min • 2π rad/1 rot • 1min/60sec = 600π/60 = 10π rad ≈ 31.4 rad

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Question 9

Define linear displacement

Answer 9

(x) a change in the linear position of an object Δx = x₂-x₁

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Question 10

Define angular displacement

Answer 10

(Θ) Angular displacement is a change in the angular position of an object.

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Question 11

Define linear velocity

Answer 11

(v) linear velocity is the rate of change in displacement over a period of time.

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Question 12

Define angular velocity

Answer 12

(ω): angular velocity is the change in angular displacement over a period of time.

Question 13

Define the following symbols used in the linear world:

1. x
2. v_TAN
3. a_TAN
4. a_c

Answer 13

1. Displacement
2. Velocity
3. Linear Acceleration
4. Centripetal acceleration

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Question 14

Define the following symbols used in the rotational world.

1. Θ
2. ⍵
3. α - ∝

Answer 14

1. Angular displacement (rad)
2. Angular velocity (rad/s)
3. Angular acceleration (rad/s²)

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Question 15

What is the relationship between V & V_TAN?

Answer 15

these two symbols are interchangeable.

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Question 16

What are the two equations for tangential velocity?

Answer 16

V_TAN = 2πr/T

V_TAN = 2πrf

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Question 17

What is the equation for centripetal acceleration?

Answer 17

a_c = V²/r

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Question 18

What is the equation for angular displacement?

Answer 18

Θ = l/r

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Question 19

what are the equations for angular velocity?

Answer 19

ω = v/r

ω = Θ/t

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Question 20

What are the equations for the angular acceleration?

Answer 20

∝ = a_TAN/r

∝ = ω/t

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Question 21

What is the equation for centripetal acceleration?

Answer 21

a_c = ω²r

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Question 22

synthesize these two ideas: Angular Displacement and Angular Velocity.

Answer 22

1: Angular Displacement and Angular Velocity are the same for every particle on the rotating object in every location. Additionally, their equations are not dependent on radius.

Question 23

synthesize these three concepts: Linear Displacement, Velocity, and Centripetal Acceleration.

Answer 23

Linear Displacement, Velocity, and Centripetal Acceleration are different for every
particle on the rotating object in every location. These vary are based on their
radii.