How Do You Calculate Arc Length and Angle Measurements in Circular Motion?

In summary, the conversation discusses the measurements and calculations related to a protractor, a phonograph record, and a circle's circumference. The protractor's scale is 7.5 cm from the center point and marked in degrees, and the question asks how far apart the marks are along the edge. The phonograph record rotates a quarter turn, equal to pi/2 radians, and the question asks how far a point on the rim has moved. Finally, the conversation also asks for the formula for the circumference of a circle in terms of its radius.
  • #1
8parks11
63
0
A protractor is made so that the edge of its scale is 7.5 cm from the center point. If the scale is marked in degrees, how far apart are the marks along the edge?

I just thought this would be 360/7.5 but it's not. I'm not sure If I got the question correct.





A 12-inchdiameter phonograph record rotatesaboutits center by one-quarter turn. a) Thorugh how many radians has it turned? b) How far has a point on the rim moved?

For a, I got pi/2 which I think iscorrect, but for b, I don't know what to do...
 
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  • #2
can i get some help?
 
  • #3
What is the circumference of a circle in terms of its radius?
 

Related to How Do You Calculate Arc Length and Angle Measurements in Circular Motion?

1. What is circular motion?

Circular motion refers to the movement of an object along a circular path, where the object's distance from a fixed point remains constant. It can be seen in various natural phenomena, such as the motion of planets around the sun, or in man-made objects like wheels and gears.

2. What is centripetal force?

Centripetal force is the force that acts towards the center of a circular path, keeping an object moving along that path. It is necessary for circular motion to occur, and its magnitude is dependent on the mass, velocity, and radius of the object.

3. How is circular motion different from linear motion?

Circular motion involves an object moving along a curved path, while linear motion involves an object moving along a straight path. In circular motion, the direction of motion is constantly changing, while in linear motion, the direction remains constant.

4. What is the relationship between centripetal force and centripetal acceleration?

Centripetal force and centripetal acceleration are directly proportional to each other. This means that as the magnitude of centripetal force increases, so does the magnitude of centripetal acceleration. This relationship is described by the formula F=ma, where F is force, m is mass, and a is acceleration.

5. How do you solve problems involving circular motion?

To solve problems involving circular motion, you can use the following steps: 1) Draw a diagram of the situation, showing the object's path and any forces acting on it. 2) Choose a coordinate system and define the direction of motion. 3) Apply Newton's laws of motion to set up equations. 4) Solve for unknown variables using appropriate formulas. 5) Check your answer and make sure it is reasonable.

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