Determine the angular acceleration of the motion, Mechanical Engineering

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.

Posted Date: 1/29/2013 7:18:27 AM | Location : United States







Related Discussions:- Determine the angular acceleration of the motion, Assignment Help, Ask Question on Determine the angular acceleration of the motion, Get Answer, Expert's Help, Determine the angular acceleration of the motion Discussions

Write discussion on Determine the angular acceleration of the motion
Your posts are moderated
Related Questions
three indications of centrifugal pump cavitating

Force on String: A string ABCD , attached to the two fixed points A and D has two weight of 1000N each attached to it at points B and C . The weights rest with portio

explain working and construction of locomotive boilers

The processing of payroll for the 10,000 workers in a large rm can either be done using 1 hour of computer time (signed by K) and no clerks or with 10 hours of clerical time (sign

types of welding, pressure and non pressure welding

Concentrate d or Point Load: How many types of load are acting on the beam? A beam is usually horizontal and the loads acting on beams are usually vertical. The followi

Which three principal possible in radial drilling machine Between them the plain drill machine, three principal movements are possible in this type of machine, by vertical move

T ota l Energy: Total energy possessed by system is the sum of all types of stored energy. Thus it will be given by E total  = PE + KE + U = mgh + 1/2mv 2  + U It is ex

Constructive Solid-Geometry Methods (CSG) Constructive models represent a solid as a combination of primitive solids. This modeling technique combine the volumes occupied by ov