Calculate Path Length of Wheel Rotation at 30°, Rad, Rev

• BunDa4Th
In summary, the question is asking for the path length traveled by a point on the circumference of a wheel with a radius of 3.7 m when the wheel is rotated through angles of 30°, 30 rad, and 30 rev. To find the answer, we can use the formula s = theta*r, where s is the path length, theta is the angular displacement, and r is the radius of the wheel. It is important to note that this question has nothing to do with angular velocity or acceleration, but rather tests our understanding of expressing angular displacement in different units.
BunDa4Th
A wheel has a radius of 3.7 m. How far (path length) does a point on the circumference travel if the wheel is rotated through angles of 30°, 30 rad, and 30 rev, respectively?

30° m
30 rev m

I really need help on this. I don't even understand what I am suppose to do because I don't really understand the question and from what the teacher told us had nothing or in anyway how to solve an equation like this.

for the first equation i tried using this
deltaTheta = w_initial*t + 1/2alphat^2 but then i realize i don't know what alpha or t is. so that's when i thought w_initial is 0 so

deltaTheta = 1/2alpha*t^2 then i got this s = theta*r which will give me time in second but not sure.

any help would be great and very helpful to my studying.

This question has nothing to do with angular velocity or acceleration. It is just to make sure you understand the various ways of expressing angular displacement.

so to find the answer would i do this

s = theta*r
Vi = W*r
a = alpha*r

finding that using kinetic formula to get distance? deltax = Vit + 1/2at^2 and v^2 = vi^2 + 2adeltaX

BunDa4Th said:
so to find the answer would i do this

s = theta*r
Vi = W*r
a = alpha*r

finding that using kinetic formula to get distance? deltax = Vit + 1/2at^2 and v^2 = vi^2 + 2adeltaX
I repeat...
OlderDan said:
This question has nothing to do with angular velocity or acceleration. It is just to make sure you understand the various ways of expressing angular displacement.
You have used one of the ways correctly.

oh okay i got it now thanks for clearing that up.

1. How do you calculate path length of wheel rotation at 30°, rad, rev?

The formula for calculating the path length of wheel rotation at 30°, rad, rev is:
Path Length = (Wheel Radius) x (Angle in Radians) x (Number of Revolutions)

2. Why is it important to calculate the path length of wheel rotation?

Calculating the path length of wheel rotation is important for various reasons. It can help in designing efficient machinery, determining the distance traveled by a vehicle or object, and analyzing the performance of a rotating system.

3. What units are used for the wheel radius and angle in the formula?

The wheel radius is typically measured in meters (m) or centimeters (cm), while the angle is measured in radians (rad). The number of revolutions is unitless.

4. How can the path length of wheel rotation be used in real-world applications?

The calculation of path length of wheel rotation can be applied in various real-world scenarios such as determining the distance traveled by a car's tires, calculating the length of a conveyor belt, and analyzing the movement of rotating parts in machinery.

5. Can the formula for calculating path length of wheel rotation be used for any type of wheel?

Yes, the formula can be used for any type of wheel as long as the radius is known and the rotation is measured in radians. It is a universal formula that can be applied to different sizes and shapes of wheels.

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