Chpt 11: Angular Kinematics

Greek Symbols

100

The value of this symbol 

σ

What is Angular Speed 

200

The value of the symbol 

φ

What is Angular distance 

300

The value of this symbol 

ω

What is Angular Velocity

400

The value of this symbol

θ

What is Angular Displacement

500

The value of this symbol and the name

α(fish)

What is Angular acceleration 

Alpha

Formulas

100

Angular distance 

_______________ =

Change in time 

whats is Angular Speed 

200

Change in angular position 

______________________  =

Change in time 

What is Angular velocity

300

Change in angular velocity

_____________________= 

Change in time 

What is Angular Acceleration? 

400

What is the formula for tangential acceleration? 

 (v2-v1)/t

500

What is the formula for radial acceleration?

v^2/r

Units

100

Whats is the unit for Revolution 

rev

200

Which angular direction is considered positive and negative

Clockwise is negative

Counter-Clockwise is positive

300

What are the units for Angular Displacement

 (rad) Radians

400

What are the units for Angular Velocity

Radians / Second

500

What are the units for Angular Acceleration

Radians / Second²

Conversions

100

How to convert radians to degrees

Radian value multiplied by 57.3

200

How to convert degrees to radians

degree value / by 57.3

300

How to convert degrees to rotations

Divide degree value by 360

400

How to convert Roations to radians

Rotation value *2π(pi)

500

How to convert Rotations to degrees

Multiply the Rotation value by 360

Problems

100

 David is fighting Goliath. If David’s 0.75-m sling is accelerated for 1.5 s at 20 rad/s2, what will be the initial velocity of the projected stone?

22.5m/s

200

The angular velocity of a runner’s thigh changes from 3 rad/s to 2.7 rad/s during a 0.5 s time period. What has been the average angular acceleration of the thigh?

−0.6 rad/s2, −34.4 deg/s2

300

The relative angle at the knee changes from 0–85° during the knee flexion phase of a squat exercise. If 10 complete squats are performed, what is the total angular distance and the total angular displacement undergone at the knee? (Provide answers in both degrees and radians.)

 Ï† = 1700°, 29.7 rad; θ = 0

400

How many revolutions are completed by a top spinning with a constant angular velocity of 3 π rad/s during a 20 s time interval?

30rev

500

A hammer is being accelerated at 15 rad/s2. Given a radius of rotation of 1.7 m, what are the magnitudes of the radial and tangential components of acceleration when tangential hammer speed is 25 m/s?

ar = 367.6 m/s2; at = 25.5 m/s2