Question

What is the displacement of a point on a wheel, initially in contact with the ground when the wheel rolls forward through half a revolution??

Answer 1

Hey Friend,

https://hi-static.z-dn.net/files/d87/b448f2563e2b27d34ec4c39d51a5d335.png

Let us consider that after half revolution, the position of the wheel has changed from C1 to C2, which on the plane surface is change from p to P2.

So, PP2 = πr

Also, πr = π metres (As r = 1m)

After half rotation, P will change to P dash,

Thus, P2Pdash = the diameter of the wheel = 2 metres.

Therefore, PPdash = √(PP2)2 + (P2Pdash)2

That is, √π2 + 22

That is, π + 4.

So the displacement of the point on the wheel is 7.143.

Hope it helps!!