Compute the angular velocity of the wheel, Mechanical Engineering

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 vB  = 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 . ωi acting at right angles to BA in the opposite direction of vA

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

Now, refer Figure (b)

 vC  = v A  + v AC

2048_Compute the angular velocity of the wheel.png

= 2.82 m / sec

Here,

θ = 45o

Likewise, refer Figure (c)

v D  = v A  + v AD

2048_Compute the angular velocity of the wheel.png

  = 4 m / sec

θ = 0o

and vE  = 2.82 m / sec

θ = 45o

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







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
Related Questions
The four masses m1, m2, m3 and m4 having their radii of rotation as 200mm, 250mm, 150mm, 250mm and 300mm are 200kg, 300kg,240kg and 260kg in magnitude respectively. The angles betw

(a) Oil, with density ρ= 900 kg/m 3 , and kinematic viscosity υ=0.00001m 2 /s, flows at the rate of 0.2m 3 /s through 500m of a cast iron pipe of diameter d=200mm. Using this infor


If Brakes Drag Causes of Problem Remedy   Insufficient pedal free play Recommended brake fluid not used

A solid shaft of diameter d is taken in power transmission. Because of modification of existing transmission system, it is needed to replace the solid shaft by a hollow shaft of th

Classification Based on Type of Welding  Fusion welding : These processes involve fusion of the base metal to complete the weld. Fusion welds generally  do  not  require  thea

ROTARY CONVERTERS Historically, these type of power sources were developed first for arc welding applications and even now these types are popular. These rotary converters are of

hardness of bore well water is less than sea water .justif

What is couple

The extent of a hazardous area depends on the rate of release, ventilation conditions, and fluid properties and is defined by the relevant regional or country standards. The pot