Posted by **HELP ME!!!!** on Sunday, November 27, 2011 at 3:05am.

speed of the car is 47.52 km/hr. a lorry wheel is rotating at 400 RPM. what is the radius (in cm) of a lorry wheel if the lorry has a same speed with the car?

- physics -
**tarun gehlot**, Sunday, November 27, 2011 at 5:19am
since car and lorry wheel has same speed

so

kinetic energy of car = rotational energy of lorry wheel

1/2mv^2= 1/2mw^2r^2

v= r w

where

w= rotational velocity

r= v/w=13.2/41.8=0.31 m= 31.5 cm

- physics -
**Damon**, Sunday, November 27, 2011 at 6:05am
I disagree.

The speed of a point on the outer edge of the lorry wheel is 47.52 km/hr

angular velocity =

400 * 2 pi radians/60 seconds

speed = angular velocity * R

so

(400* 2/60) pi R = (47.52*10^3/3600)meters/second

- physics -
**drwls**, Sunday, November 27, 2011 at 8:30am
I don't see any disagreement. Both previous responders use V = R*w.

Tarun has already correctly converted V to m/s and w to rad/s. (Actually, I get 41.88 rad/s for w).

The land speed of a point on a rolling wheel depends upon the location. It equals V (vehicle velocity) at the axle, 0 at the point of contact with the ground (the "instant center" of rotation) and 2V at the top edge of the tire.

- physics -
**Damon**, Sunday, November 27, 2011 at 8:59am
I disagree that the kinetic energy of the car is equal to the kinetic energy of the lorry wheel :)

- physics -
**drwls**, Sunday, November 27, 2011 at 9:09am
I agree with Damon's last statement about kinetic energy.

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