Determine the angular acceleration of the motion, Mechanical Engineering

Assignment Help:

Determine the angular acceleration of the motion:

A flywheel of mass 15 kg and radius 20 cm is wound by a rope that carries a weight A of mass 5 kg at its free end as illustrated in Figure. Determine the angular acceleration of the motion, supposing gravitational acceleration = 10 m/sec2 for purpose of simplified calculations, and letting the following two cases:

(i) If friction at the bearing of flywheel-shaft is zero.

(ii) If frictional couple developed at the bearing of shaft is 2 N-m.

Solution

While block A travels a distance s downward, this has certain linear velocity V and acceleration a. The equivalent angular velocity ω and angular acceleration α of the flywheel of radius (r = 0.2 m) are specified by

V = r ω = 0.2 ω

a = r α = 0.2 α

s = r θ

Here, θ is the angular displacement of the flywheel. Likewise to equation in linear motion given by

                                            V 2 = 2 a s

The equation in angular velocity is

                                           ω2 = 2 α θ

By using principle of conservation of energy letting datum level as A′ which is the final position of A, we have

WA   × s = W V 2  /2g + Im  ω2  /2+ C × θ

 (i)        While frictional couple C = 0;

5 × 10 × (0.2 θ) = 5 (0.2)2/2  ω2 + 15 (0.2)2  /2 × ω2/2  + 0

10 ×θ = ω2 × (0.2) 2 /2[5 + 7.5]

10 ×θ = α θ × (0.2)2 × 12.5

∴ α = 20 rad / sec 2.

 (ii)  50 × 0.2 θ = α θ (0.2)2 × 12.5 + 2 × θ

∴ α = 16 rad / sec2.


Related Discussions:- Determine the angular acceleration of the motion

Oxides, Oxides These comprise alumina, magnesia, thoria, beryllia and ...

Oxides These comprise alumina, magnesia, thoria, beryllia and zirconia. Other oxides that are utilized sparingly due to high cost comprise hafnia, ceria and yttria. Variety of

Beee, Explain the construction and principles of operations of induction mo...

Explain the construction and principles of operations of induction motor

Pendulum pump mechanism, describe about pendulum pump mechanism and dia...

describe about pendulum pump mechanism and diagram

Meaning, What different of blow hole and pin hole

What different of blow hole and pin hole

Inspection of fasteners of motorcycle, Inspection of Fasteners: The motorc...

Inspection of Fasteners: The motorcycle carries number of nuts and bolts. They should be properly tightened for the smooth running of motorcycle. All fasteners are checked

Effect of the wet and dry curing methods on the strength, Effect of curing ...

Effect of curing conditions on strength, porosity, absorptivity, and shrinkage of concrete in hot and dry climate Abstract This term paper will study the effect of the wet a

Mechanical vibrations, The suspension system of a car is modelled as having...

The suspension system of a car is modelled as having an effective stiffness of 5x10 6 (N/m) and an effective mass of 750 (kg). The car is travelling over a road with bumps that ca

Mechanical properties of high temperature strength of metals, Q. Mechanical...

Q. Mechanical Properties of high temperature strength of metals? The high temperature strength of metals is related to their melting points, but many other factors limit the pr

Explain about wire-frame model, Q. Explain about wire-frame model? A wi...

Q. Explain about wire-frame model? A wire-frame model of an object is the simplest, but more verbose, geometric model that can be used to represent it mathematically in the com

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd