Question

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?

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

I disagree that the kinetic energy of the car is equal to the kinetic energy of the lorry wheel :)

Answer 5

I agree with Damon's last statement about kinetic energy.