Calculating the Radius of a Rotating Wheel Using Radians and Arc Length

In summary, when a wheel is rotated through an angle of 35o, a point on the circumference travels through an arc length of 2.5m. Using the equation r = DeltaS / Delta Theta, the radius of the wheel is found to be 4.1m. The additional information about angles in radians and revolutions is not relevant to finding the radius.
  • #1
Unity
4
0

Homework Statement


When a wheel is rotated through an angle of 35o, a point on the circumference travels through an arc length of 2.5m. When the wheel is rotated through angles of 35 radians and 35 revolutions, the same point travels through arc lengths of 143m and 9.0 x 102m, respectively. What is the radius of the wheel?

DeltaS = 2.5m
DeltaTheta = 35o
r = ?

Homework Equations


r = DeltaS / Delta Theta


The Attempt at a Solution


Okay, so first i converted 35o to radians and came out with .61 radians.
(35o x Pie) / 180o = .61 radians

Next I plugged the variables into the equation.
2.5m / .61 radians = 4.1m. Thus 4.1 being the radius.
My main concern is the other information that i was given, is it relevant to the problem? Or is it simply extra information?
Thanks in advance!
 
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  • #2
Hi Unity, welcome to PF.
As you have said, the first information is sufficient to find the radius.
 
  • #3
Thanks for the answer man. I'll definantly be sticking around. :approve:
 

FAQ: Calculating the Radius of a Rotating Wheel Using Radians and Arc Length

1. What is a radian and how does it differ from degrees?

A radian is a unit of measurement for angles, just like degrees. However, while a degree is based on dividing a circle into 360 equal parts, a radian is based on dividing a circle into 2π (approximately 6.28) equal parts. In other words, a full circle is equal to 2π radians or 360 degrees.

2. How do you convert between radians and degrees?

To convert from radians to degrees, multiply the radian measurement by 180/π. To convert from degrees to radians, multiply the degree measurement by π/180. For example, to convert 2 radians to degrees, you would do: 2 x (180/π) = 114.59 degrees.

3. What is angular motion and how is it different from linear motion?

Angular motion is the movement of an object along a circular path. It is different from linear motion, which is the movement of an object in a straight line. In angular motion, the object travels at a constant speed but changes direction constantly, while in linear motion, the object travels at a constant speed in a single direction.

4. What is angular velocity and how is it related to angular motion?

Angular velocity is a measure of how fast an object is rotating around a fixed point. It is related to angular motion because it is a measure of the rate at which an object is changing its angular position. It is also influenced by the object's angular acceleration, which is the rate at which its angular velocity is changing.

5. How are radians and linear distances related?

Radians and linear distances are related through the radius of a circle. The length of an arc in radians is equal to the radius of the circle multiplied by the angle in radians. So, for example, if the radius of a circle is 5 meters and the angle is 2 radians, the length of the arc would be 5 x 2 = 10 meters.

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