**How to Calculate Tangential Speed from Revolutions**A carnival ride spins people around in a circle that has a radius of 5 meters. The carnival ride can make 20 revolutions per minute. One day, little Timmy is riding the ride when suddenly he slips out of his harness and flies off (don’t worry, he lands in cotton candy and is perfectly fine)! How fast was little Timmy initially moving when he slipped out of his harness?**Options:**- 13.67- 8.55- 16.47- 10.47### Step-by-step Solution:1. **Identify Given Values:** - Radius (r) = 5 meters. - Revolutions per minute (RPM) = 20.2. **Convert RPM to Angular Velocity:** - First, convert revolutions per minute to radians per second. - 1 revolution = \(2\pi\) radians. - Angular velocity (ω) in radians per second can be calculated as: \[ \omega = \text{RPM} \times \frac{2\pi\ \text{radians}}{1\ \text{revolution}} \times \frac{1}{60\ \text{seconds}/\text{minute}} = 20 \times \frac{2\pi}{60} = \frac{40\pi}{60} = \frac{2\pi}{3}\ \text{radians/second} \]3. **Calculate Tangential Speed (v):** - Tangential speed can be calculated using the formula: \[ v = r \times \omega \] - Plug in the values: \[ v = 5\ \text{meters} \times \frac{2\pi}{3}\ \text{radians/second} = \frac{10\pi}{3}\ \text{meters/second} \] - Since \(\pi \approx 3.14\), \[ v \approx \frac{10 \times 3.14}{3} \approx \frac{31.4}{3} \approx 10.47\ \text{meters/second} \]Thus, little Timmy was initially moving at approximately 10.47 meters per second when he slipped out of his harness.### Answer

Write the given values with the suitable variables. r=5 mω=20 rev/min=20×2π60 rad/s=2.094 rad/s…

A carnival ride spins people around in a circle that has a radius of 5 m. The carnival ride can make 20 revolutions per minute. One day, little Timmy is riding the ride when suddenly he slips out of his harness and flies off (don't worry, he lands in cotton candy and is perfectly fine)! How fast was little Timmy initially moving when he slipped out of his harness? 13.67 8.55 16.47 10.47

A carnival ride spins people around in a circle that has a radius of 5 m. The carnival ride can make 20 revolutions per minute. One day, little Timmy is riding the ride when suddenly he slips out of his harness and flies off (don't worry, he lands in cotton candy and is perfectly fine)! How fast was little Timmy initially moving when he slipped out of his harness? 13.67 8.55 16.47 10.47

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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