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A wheel is rolling along a straight path without slipping. Determine velocity of points A, B and P. OP=600mm,ω=4rad/sec,V0=4m/s

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VA=?,VB=?OP=600mm,VP=?

ω=4rad/s,V0=4m/s

Instantaneous centre of wheel is at point of contact.

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V0=I0.wI0=V0w=44=1m=1000mm

ID = Radius = 1000mm

IA = D = 2000 mm

And IB=10002+10002=1414.2mmVA=IA.ω=2000×4=8000mm/s=8m/sVB=IB.ω=1414.2×4=5656.8mm/s=5.6568m/sPOI=90+20=1100

By cosine rule,

IP=(OP2+OI22.OP.OI.cosPOIIP=6002+100022×600×1000cos1100=1400mVP=IP.W=1400×4=5600m/s=5.6m/s

Instantaneous velocity of A=8m/s

Instantaneous velocity of B=5.6568m/s

Instantaneous velocity of C=5.6m/s

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