Angular speed of the cylinder, Mechanical Engineering

Angular speed of the cylinder:

A cylinder of mass 70 kg rotates from rest in frictionless bearing under the action of a mass of 7.0 kg carried by a rope wrapped around the cylinder. If the diameter is 1000 mm, what will be the angular speed of the cylinder, 2 seconds after motion starts.


Free body diagrams of the cylinder and the mass are shown in Figures (b) and (c). We should keep in mind that the tension in the rope is similar for both the diagrams.

Let the cylinder rotate in a clockwise direction such that the mass m shall move downwards. Let a be the downward acceleration of mass m and α be the angular acceleration of the cylinder. Then we may write a = rα , where r is the radius of the cylinder.

Inertia force Fi  = m a shall be acting upwards on the mass m as shown in Figure (c).

Likewise, inertia couple M i  = Iα shall be acting on the cylinder in the anticlockwise direction. This is shown in Figure (b).

Now we write down dynamic equilibrium equation for the mass and we get

T + ma = mg

or, T = mg - ma = 7 × 9.81 - 7a

Likewise equilibrium of moments for the cylinder will give us,

T . r - I α = 0

∴ (7 × 9.81 - 7 a) × 0.5 =( ½) × 70 × 0.52 × α

∴ (68.67 - 7 × 0.5 α) 0.5 = 35 × 0.52  × α

or,        34.34 - 1.75 α = 8.75 α

∴ α = 3.27 rad / sec 2 .

To attain angular velocity of the cylinder after 2 seconds, we simply write kinematic equation, knowing that ω0 = 0 .

∴ ω = ω0 + α t = 0 + 3.27 × 2 = 6.54 rad / sec .

Posted Date: 1/29/2013 6:31:57 AM | Location : United States

Related Discussions:- Angular speed of the cylinder, Assignment Help, Ask Question on Angular speed of the cylinder, Get Answer, Expert's Help, Angular speed of the cylinder Discussions

Write discussion on Angular speed of the cylinder
Your posts are moderated
Related Questions

Q. Describe about Carbon Steel? Steel having no specified minimum quantity for any alloying element (other than commonly accepted amounts of manganese, silicon, and copper) and

Process capability Process capability which is a measurement with respect to the inherent precision of a manufacturing process has two significant elements, i.e. process facto

Closed System: The system that can exchange energy with the surrounding but not the mass. The quantity of matter hence remains fixed. And the system can be described as cont

A semi-elliptic multi-leaf spring is needed for the suspension of the rear axle of a truck. It consists of two extra full-length leaves and ten graduated length leaves including th

Direct Current ( DC ) :  The direct current flows through a wire in one direction and it remains same over time. The current from battery is always direct current. Direc

A special feature of the PDES A special feature of the PDES development is the use of the formal language EXPRESS for modeling the product information. There will be capabiliti

Can you prove an equation from Plane Stress and Plane strain?

Determine the maximum stress intensities: A rolled steel I-section, flanges 150 mm wide & 25 mm thick, web 200 mm long & 10 mm thick  is utilized to carry & axial load of 800

A truss of 12 m span is loaded as shown in figure below. Determine the forces in the members of the truss by method of sections.