Linear and Angular Velocity number# 15 PDF

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Summary

Engineering Mechanics Lab theory for helping made a particles ...

Description

Theory Define linear velocity. A vector quantity that denotes the rate of change of position with respect to time of the object’s center of mass. The formula of linear velocity is

v=x/t Where “v” is the velocity, “x” is the total distance covered and "t" indicates the amount of time.

Define Angular velocity. A vector quantity describing an object in circular motion, its magnitude is equal to the speed of the particle and the direction is perpendicular to the plane of its circular motion. OR Angular velocity ω as the rate of change of an angle. In symbols, this is

ω=Δ θ/Δ t Angular velocity ω is analogous to linear velocity v.

Relation between linear velocity & Angular velocity:

Fig# 01 Velocity =

displacement time

v=

ds dt

ds = vdt ----------- equation A ds = rdθ

So that s = r θ

Putting value ‘ds’ in equation A rdθ = vdt dθ dt

=

v 𝑟

Putt value ‘𝜔’ v

𝜔=𝑟

So that 𝜔 =

dθ dt

We can write this relationship in two different ways:

v = r ω or ω =

v r

Derivation of Linear & Angular Velocity: Vf ˗ Vi

a=

t Vf

a=

t V

a=

t

v = at Using equation of motion

-------------

equation 1

1

h = 2 a𝑡 2 + vo 𝑡

2h t2 Using equation 1 and putt value “a” a=

v = at v=

2h

×t

t2

v=

2h

---------------

t

equation A

Using relation of linear & angular velocity and putt value of equation A

v=rω rω= ω=

2h

t 2h

tr ωt h = 2 r

constant =

h r...