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
Mr. Moody has decided to invest at most N$100 000 in securities in the form of corporate stocks. He has classified his options into three groups of stocks: blue-chip stocks that he

Illustrate the Centrifugal Clutch in Detail with neat sketch ? Illustrate the Electromagnetic Clutch in Detail with neat sketch ? Illustrate the Diaphragm spring Clutch in

Calculate for spring amount of load carried: The table below gives specific of a compound spring consisting of two co-axial close-coiled springs. If the spring is subjected to


This components extensively used teh specialized and / or general purpose software. Often it may development for typical application and to perform calculations in the design

Gas Flow Rates Shielding gas flow requirements are based on cup & nozzle size, weld pool size & air movement . Generally, the flow rate increases in proportion to the cross s

Supports for Rigid Bodies (Space Structures): The primary step in solving equilibrium problems is to draw free-body diagram. Isolate the body through its surrounding. Replace

how will u designate a v belt

how to calculate machining time for milling operation

velocity of belt: velocity of belt passing over the driver pulley will decrease Now with this velocity belt pass over driven pulley, Now Velocity of Driven = Velocity