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scoutfai
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The question is : The speed of a car traveling on a straight horizontal road is V. What is the speed of the point P on the tyre of the car ?
(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 don't understand what he doing) my teacher method..
i will show both methods mentioned above, i hope any expert can give me a better explanation 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.
(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 don't understand what he doing) my teacher method..
i will show both methods mentioned above, i hope any expert can give me a better explanation 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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