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?
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
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
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.
I disagree that the kinetic energy of the car is equal to the kinetic energy of the lorry wheel :)
I agree with Damon's last statement about kinetic energy.
To find the radius of the lorry wheel, we need to consider the relationship between the speed of the car and the rotation of the wheel.
First, let's convert the car's speed from kilometers per hour (km/hr) to centimeters per minute (cm/min). Since we need both values to be in the same unit, we will use minutes to match the RPM of the wheel.
1 kilometer = 100,000 centimeters (cm)
1 hour = 60 minutes
So, the car's speed can be converted as follows:
47.52 km/hr = 47.52 * 100,000 cm / 60 min ≈ 79,200 cm/min
Now, let's relate the speed of the car to the rotation of the lorry wheel. The circumference of a circle is given by the formula:
Circumference = 2 * π * radius
The lorry wheel completes 400 rotations per minute (RPM). If we multiply the circumference by the number of rotations, we will get the distance that the lorry wheel covers in one minute.
Distance covered by the lorry wheel in one minute = 400 * Circumference
Now, we can substitute the values we have and solve for the radius.
Distance covered by the lorry wheel in one minute = 400 * (2 * π * radius)
Since the car and the lorry have the same speed, the distance covered by the lorry wheel in one minute should be equal to the car's speed, which is 79,200 cm/min.
Therefore, we can set up the equation:
79,200 = 400 * (2 * π * radius)
Now, let's solve for the radius:
1. Divide both sides of the equation by 400:
79,200 / 400 = 2 * π * radius
2. Simplify:
198 = 2 * π * radius
3. Divide both sides by 2 * π:
198 / (2 * π) = radius
4. Calculate:
radius ≈ 31.51 cm
Therefore, the radius of the lorry wheel is approximately 31.51 cm.