Find the magnitude of the angular acceleration of system, Mechanical Engineering

Find the magnitude of the angular acceleration of system:

A homogeneous sphere having a mass of 100 kg is associated to a slender rod having a mass of 20 kg. In the horizontal position, the angular speed of the system is 8 rad/sec. calculate the magnitude of the angular acceleration of the system and the reaction at O on the rod.

Solution

The system shall be rotating about O as shown in the figure. First let us try to locate the mass centre of the system.

∴ x¯ = (20 × 300 + 100 × 750) /120

= 675 mm .

The position of the mass centre is shown in the free body diagram in Figure (b). All the forces acting on the system are illustrated on FBD.

External forces are reactions at O, i.e. OT and ON and gravitational force mg shall be acting through the mass centre. r ω2 and r α shall be normal and tangential components of acceleration and mr ω2 and mr α are initial forces in these respective directions.

The total moment of inertia I equals the moment of inertia of the rod about its end ( 1/3) ml2  plus the transferred moment of inertia of the sphere, that means

               ( 2/5) mr 2  + md 2

where, d = 750 mm = 0.75 m

∴ I = (1/3) 20 (0.6)2  + (2/5) 100 (0.15)2  + 100 (0.75)2

= 59.55 kg m 2 .

Now apply dynamic equilibrium equations. ∑ M o  = 0 shall give us magnitude of α.

∴ ∑ M - I α = 0

∴ 120 × 9.8 × 0.675 = 59.55 α

∴ α = 13.3 rad / sec 2 .

Now, ∑ Fx = 0 . Thus, the sum of the forces on horizontal axis,

- ON + m r ω2 = 0

∴ ON = 120 × (0.675) (8)2 = 5180 N         to the left.

And,

∑ Fy = 0

- OT - mg + mr α = 0

∴ OT= mg - mr α

= 120 × 9.8 - 120 × 0.675 × 13.3

∴ OT = - 98.7 N.

Thus, direction of OT is upwards.

Posted Date: 1/29/2013 6:33:07 AM | Location : United States







Related Discussions:- Find the magnitude of the angular acceleration of system, Assignment Help, Ask Question on Find the magnitude of the angular acceleration of system, Get Answer, Expert's Help, Find the magnitude of the angular acceleration of system Discussions

Write discussion on Find the magnitude of the angular acceleration of system
Your posts are moderated
Related Questions
a steel bar is 900 mm long

For an automotive component of your choice that is traditionally metallic, review how it could be re-engineered as a composite? How factors such as fibre & matrix type, fibre volum

Perfect Frame - Truss: Perfec t Frame The frame that is composed of such members, which are sufficient to keep the frame in equilibrium, when the frame is sustaining the

Q. What do you understand by Carburization? Carburization is initiated by the adsorption of carbon in contact with the surface of the metal and may progress by diffusion along

Short Circuiting Transfer The short circuiting transfer  occurs when the welding current and the arc voltage is low. Metal is transferred from the electrode to the work only wh

How di i get the volume of a regular pentagon if the given was a height of 9", a base of 3" and a central angle of 75

Find out the product of inertia of a rectangular area: Find out the product of inertia of a rectangular area b × d with respect to its sides as illustrated in Figure Solut

Example of support reaction: A fixed crane of 1000Kg mass is to lift 2400Kg crates. It is held in place by pin at point A and a rocker at point B . the C . G . is located

(a) Split up the harmonic x = 8 sin(ωt + 45°), into two harmonic motions, one of which has amplitude of 10 and phase difference zero. (a) A body is subjected to two harmonic mot

Describe the internal structure, bonding of atoms and molecules and to understand the mechanical properties of materials. Comprehensive understanding of properties of materials, at