Angular Motion

 


1) Rotational distance

 


WHERE :

S = Rotational distance 

r = Radius 

θ(rad) = Turning angle 

 

NOTE: Here the angle is measured by radiant.

 

©Equatcy

 

2) Angular velocity

 


WHERE :

ω = Angular velocity 

t = Time 

θ(rad) = Turning angle

 

NOTE: Angular velocity is the rate at which angular displacement changes.

 

©Equatcy

 

3) Periodic period

 


WHERE :

ω = Angular velocity 

T = Periodic period 


NOTE: Periodic period is the period of time required for an object to travel one full round.

 

©Equatcy


4) Frequency

 


WHERE :

f = Frequency 

T = Periodic period 


NOTE: Frequency is the number of rounds an object rotates in a second. The unit of frequency is Hz .

 

©Equatcy

 

5) Relationship between frequency and angular velocity

 

ω = 2 π f

 

WHERE :

f = Frequency 

ω = Angular velocity 

 

NOTE: The relationship between frequency and angular velocity is used in many practical situations. This formula can also be used to determine the rpm value of a motor.

 

©Equatcy

 

6) Relationship between linear velocity and angular velocity

 

V = r ω

 

WHERE :

V = Linear velocity 

ω = Angular velocity 

r = Radius 

 

NOTE: Any object engaged in a rotational motion has a linear velocity along the tangent to the motion.

 

©Equatcy

 

7) Angular acceleration

 


WHERE :

ω- ω(0) = Angular velocity difference 

t = Time 

α = Angular acceleration 

 

NOTE : Angular velocity is the rate at which angular velocity changes.


©Equatcy


8) Relationship between linear acceleration and angular acceleration

 

a = r α

 

WHERE :

a = linear acceleration 

α = angular acceleration 

r = Radius 


NOTE: If an object in rotational motion rotates at angular acceleration, it has tangential acceleration in the direction of contact.

 

©Equatcy

 

9) Equations related to rotational motion

 


WHERE :

ω = Last Angular velocity 

ω(o) = First Angular velocity 

θ = Angular displacement (

t = Time 

α = Angular acceleration 


NOTE : Motion equations are used in both linear motion and angular motion.

 

©Equatcy

 

10) Uniform Angular Motion Equation


θ = ω t


WHERE :

θ = Angular displacement 

ω = Angular velocity 

t = Time 

 

NOTE: This equation is used for uniform rotational motion.

 

©Equatcy

 

11) Rotational inertia



WHERE :

I = Rotational inertia 

m = Mass 

r = Perpendicular distance from the axis of rotation 

 

NOTE : In this case, in order to find the moment of inertia of an object, it is necessary to find the sum of the inertial averages produced by each of them separately.


©Equatcy

 

12) Angular momentum


L = I ω

 

WHERE :

L = Angular momentum 

ω = Angular velocity

I = Rotational inertia 

 

NOTE: Angular momentum is the fullness of linear momentum.

 

©Equatcy

 

13) Torque

 

ζ = I α

 

WHERE :

ζ = Torque 

α = Angular Acceleration 

I = Rotational inertia 

 

NOTE: The ability to rotate an object is Torque. Whenever there is an angular acceleration the object must have a Torque.


©Equatcy

 

14) Rotational work

 

W = ζ θ

 

WHERE :

ζ = Torque 

θ = Angular displacement 

W = Rotational work 

 

NOTE: The problem is solved by combining angular motion with linear motion.

 

©Equatcy

 

15) Rotational kinetic energy

 


WHERE :

E = Rotational kinetic energy 

I = Rotational inertia 

ω = Angular velocity 

 

NOTE : The problem is solved by combining angular motion with linear motion.

 

©Equatcy

 

16) Rotary power

 

P = ζ ω


WHERE :

ζ = Torque 

ω = Angular velocity 

P = Rotary power 

 

NOTE: The problem is solved by combining angular motion with linear motion.

 

©Equatcy

 

17) Center convergence acceleration

 


WHERE :

a’ = Center convergence acceleration 

r = Radius 

ω = Angular velocity

v = Tangential velocity

 

NOTE : The acceleration created by the change in velocity of a rotational motion is the Center convergence acceleration.


©Equatcy

 

18) Center convergence force

 

F = m V ω


WHERE :

F = Center convergence force 

ω = Angular velocity 

V = Tangential velocity 

m = Mass (

 

NOTE: The center convergence acceleration is substituted for the acceleration of the equation F = m a.

 

©Equatcy

 

Post a Comment

Previous Post Next Post