Compute the angular velocity of the wheel:

A wheel of 0.5 m radius rolls over a horizontal surface without slipping as illustrated in Figure (a). The velocity of its centre is 2 m/sec and is constant. Compute the angular velocity of the wheel and velocities at C, D and E.

Solution

As the wheel rolls on the ground and does not slip or slide on the ground, the velocity of the point of contact of wheel with ground is same but the velocity of ground should be equal to zero.

∴          we get v_B  = 0

Now consider the wheel as the rigid body and the body rotating about an axis through the pole A and B is the point on the rim of the wheel.

Considering this motion as a plane motion, we have

v _B  = v _A  + v _AB  = 0

∴ v _A  = - v _AB

 = - A B . ω_i acting at right angles to BA in the opposite direction of v_A

∴  v _A /AB  = ω = 2 /0.5= 4 rad / sec. (numerically)

Now, refer Figure (b)

 v_C  = v _A  + v _AC

= 2.82 m / sec

Here,

θ = 45^o

Likewise, refer Figure (c)

v _D  = v _A  + v _AD

  = 4 m / sec

θ = 0^o

and v_E  = 2.82 m / sec

θ = 45^o

Posted Date: 1/29/2013 2:05:21 AM | Location : United States

Ask an Expert

Related Discussions:- Compute the angular velocity of the wheel, Assignment Help, Ask Question on Compute the angular velocity of the wheel, Get Answer, Expert's Help, Compute the angular velocity of the wheel Discussions

Write discussion on Compute the angular velocity of the wheel
Your posts are moderated

Write your message here..

Related Questions

Simple single machine system, Consider a simple single machine system. It c... Consider a simple single machine system. It consists of workpieces that enter the system, wait their turn to be processed on a single machine, and then depart the system. The workp

Air injection system and solid injection system, (a) Explain a typical fuel... (a) Explain a typical fuel feed system for a C.I engine, differentiate between air injection system and solid injection system. (b) Why Gasoline injection system has been adopte

Metal transfer in co2 welding, METAL TRANSFER IN CO2 WELDING In CO 2 wel... METAL TRANSFER IN CO2 WELDING In CO 2 welding, two distinct types of metal transfers are identified viz. short circuiting transfer and free flight globular transfer. Short Cir

Elastomers, define elastomer.explain in details? define elastomer.explain in details?

Polymerization, Polymerization Whether similar molecules join in long ... Polymerization Whether similar molecules join in long chain is termed as polymerization and resulting outcome is a polymer in a chemical reaction. Each plastic are polymers. T

Characterised punching shear failure in bearing capacity, How can punching ... How can punching shear failure are characterised in bearing capacity? Punching Shear Failure This mode of failure is characterised by large deformations beneath the footing

Planning a retail interior space, Question 1: A good display of the mer... Question 1: A good display of the merchandise is the result of planning, cooperation and coordinating. A good schedule of work is important for a good design with the use of me

Maximum Shear Stress theory , A steel plate with dimension shown in sketch ... A steel plate with dimension shown in sketch (a) below is subjected to P = 150 kN tensile force and M= 300 N-m bending moment. The plate is made of AISI 1080 steel. A hole is to be

Moment of intertia, define moment of inertia define moment of inertia

How is metal removed in metal cutting, How is metal removed in metal cuttin... How is metal removed in metal cutting ? Explain the process by giving simple model to explain the metal removed process. What are the different conditions that could allow a con