Question

A child is spinning a rock at the end of a rope at a rate of 200 revolutions per minute. at the moment they release the rope, the rock's linear speed is 525 feet per minute. what is the length of the rope the child was spinning?

Answer 1

Step-by-step explanation:To find the length of the rope the child was spinning, you can use the relationship between linear speed, angular speed (revolutions per minute), and the radius of the circular motion.

The formula for the linear speed (v) of an object in circular motion is given by:

v = ω * r

Where:

- v is the linear speed (525 feet per minute in this case).

- ω (omega) is the angular speed in radians per minute.

- r is the radius of the circular motion (the length of the rope in this case).

First, you need to convert the angular speed from revolutions per minute to radians per minute. There are 2π radians in one revolution, so:

ω = 200 revolutions/minute * 2π radians/revolution = 400π radians/minute

Now, you can use the linear speed and angular speed to find the radius (length of the rope):

525 feet/minute = (400π radians/minute) * r

Now, solve for r:

r = 525 feet/minute / (400π radians/minute)

r ≈ 0.418 feet/minute

So, the length of the rope the child was spinning is approximately 0.418 feet (or about 5.016 inches).