The question is : The speed of a car travelling on a straight horizontal road is V. What is the speed of the point P on the tyre of the car ?(adsbygoogle = window.adsbygoogle || []).push({});

(A) 0.5V (B) V (C) 2V (D) 3V

i got try to solve it myself, and i get the answer (B)....

However, my teacher do it and get answer (C)....

i am not confidence with my method, but i also not agree with (or i should say i dont understand what he doing) my teacher method..

i will show both methods mentioned above, i hope any expert can give me a better explaination and calculation. U help is meaningful to me !

My method :

Since the speed of the car is V, hence the speed of the centre of the wheel is also V.

let the speed of the point P be X, now we should find X in term of V.

X = linear velocity of point P

X = rw where r = radius of wheel and w = angular velocity of the wheel

we know w = 2(pi) / T , this mean in time T, the wheel make one complete revolution.

In time T also, the wheel move horizontally with distance 2(pi)r

since speed = distance / time, hence V = 2(pi)r / T

thus T = 2(pi)r / V

therefore w = 2(pi) / T

= 2 (pi) / {2(pi)r / V }

= 2V(pi) / [2r(pi)]

= V / r

so X = rw = r ( V/r )

X = V

Do u agree with my method ? if not, please tell me why !

My teacher method is :

from the diagram, let the centre of the wheel be O and the line joining the point P and O will intercept with the point on the ground ( the tangential point of the wheel surface to the ground ) where the wheel touch the ground.

so, let this point called as Q.

the distance QO = r

distance QP = 2r

from V = rw where v = linear velocity, r = radius of the body , w = angular velocity, hence V is direct proportional to r

so V / r = constant

so { V / r for point O } = { V / r for point P }

if the V of P = x, then x / 2r = V / r

x = (v/r)(2r)

x = 2v

do u agree with my teacher method ? if you say yes, please explain to me why my teacher can use the point Q as the point of axis of rotation of the wheel. If you say no, tell me your reason also. Thanks you, u help is meaningful to me.

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# Homework Help: Circular motion of a wheel

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