A wheel is rolling along a straight path without slipping. Determine velocity of points A, B and P. $OP = 600 mm, \omega = 4 rad/sec, V

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written 7.9 years ago by

teamques10 ★ 68k

$$V_A= ?,V_B= ?OP=600mm,V_P= ?$$

$ω = 4 rad/s , V_0 = 4m/s$

Instantaneous centre of wheel is at point of contact.

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$V_0=I_0.w \\ ∴I_0 = \dfrac {V_0} w = \dfrac 44=1m=1000mm $

ID = Radius = 1000mm

IA = D = 2000 mm

And $I_B=\sqrt{1000^2+1000^2} =1414.2 mm \\ V_A=IA.ω=2000×4=8000mm/s=8 m/s \\ V_B=IB.ω=1414.2×4=5656.8 mm/ s=5.6568 m/ s \\ ∠POI=90+20=110^0 $

By cosine rule,

$IP=\sqrt{(OP^2+OI^2-2.OP.OI.\cos ∠POI } \\ IP=\sqrt{600^2+1000^2-2×600×1000 \cos 110^0 }=1400 m \\ V_P=IP.W=1400×4=5600 m/s=5.6 m/s $

Instantaneous velocity of $A=8 m/s $

Instantaneous velocity of $B=5.6568 m/s$

Instantaneous velocity of $C=5.6 m/s $

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