Calculating Revolutions: Sam's Lost Ring in the Mall - Homework Help

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In summary, the formula for calculating revolutions is Number of revolutions = Distance traveled / Circumference of the object. To calculate distance traveled, you need to know the speed of the object and the time it took to travel that speed, using the formula Distance traveled = Speed x Time. The circumference of an object can be calculated using the formula Circumference = 2 x Pi x Radius. Knowing the number of revolutions an object has completed can help estimate the distance traveled and locate a lost object. Real-life applications of calculating revolutions include engineering, physics, and sports.
  • #1
blink1987
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Homework Statement


Sam drops his ring in the mall. It goes rolling away from him at a velocity of 3.0 m/s. It has a radius of 0.50cm. After rolling 1.0 m how many revolutions has it made?


Homework Equations


vcm= rw


The Attempt at a Solution


vcm
3.0x 2 pi = 18.84
0.50x 18.84= 9.42
 
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  • #2
Welcome to PF.

How do you see the velocity affecting the number of revolutions?

If the circumference is 2*.5*π ... or π cm, then isn't the number of revolutions the number of circumferences it has traversed? 100 cm / π cm ?
 
  • #3


Based on the given information, we can use the equation v= rw to calculate the number of revolutions the ring has made after rolling 1.0 m. First, we need to convert the velocity from 3.0 m/s to radians per second by multiplying it by 2 pi. This gives us a velocity of 18.84 radians/s. Next, we can use the radius of 0.50 cm to calculate the circumference of the ring, which is 2 pi times the radius. This gives us a circumference of 9.42 cm. Finally, we can divide the distance traveled (1.0 m) by the circumference to get the number of revolutions. 1.0 m / 9.42 cm = 0.106 revolutions. Therefore, after rolling 1.0 m, the ring has made approximately 0.106 revolutions. It is important to note that this is an approximation since the given radius is in centimeters and the distance traveled is in meters.
 

What is the formula for calculating revolutions?

The formula for calculating revolutions is Number of revolutions = Distance traveled / Circumference of the object. This formula is used to determine the number of times an object has completed a full rotation.

How do you calculate distance traveled?

To calculate distance traveled, you need to know the speed of the object and the time it took to travel that speed. The formula is Distance traveled = Speed x Time. This formula assumes that the speed remains constant throughout the journey.

What is the circumference of an object?

The circumference of an object is the distance around the outside edge of the object. It can be calculated using the formula Circumference = 2 x Pi x Radius. Pi is a mathematical constant equal to approximately 3.14, and the radius is the distance from the center of the object to the edge.

How can revolutions be used to find a lost object?

If you know the number of revolutions an object has completed, you can use it to estimate the distance traveled and the approximate location of a lost object. By calculating the circumference of the object and dividing the distance traveled by it, you can determine the number of revolutions. This can help narrow down the search area for a lost object.

What are some real-life applications of calculating revolutions?

Calculating revolutions is used in various fields, such as engineering, physics, and sports. In engineering, it is used to determine the speed and efficiency of machines. In physics, it is used to study the motion of objects. In sports, it is used to measure the performance of athletes, such as the number of rotations in figure skating or diving.

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