How Does Circular Motion Impact Calculations in Physics Problems?

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SUMMARY

This discussion focuses on the application of circular motion concepts in physics problems, specifically involving angular velocity and centripetal force calculations. The user attempts to solve various problems, including determining the angle of a speck on a turntable rotating at 85 rpm, calculating the speed of a roller coaster at the bottom of a dip, and finding the orbital period of a satellite moving at 5247.66 m/s. Key equations discussed include angular velocity calculations and the formula for orbital period, T = 2(pi) * sqrt(r^3 / GM), where G is the gravitational constant and M is the mass of the Earth.

PREREQUISITES
  • Understanding of angular velocity and its calculation
  • Familiarity with circular motion dynamics
  • Knowledge of gravitational force and orbital mechanics
  • Ability to convert between different units of measurement (e.g., rpm to rad/s)
NEXT STEPS
  • Learn how to calculate angular displacement in circular motion problems
  • Study centripetal acceleration and its relationship to speed and radius
  • Explore the concept of effective weight in non-inertial frames, such as roller coasters
  • Investigate the derivation and application of Kepler's laws of planetary motion
USEFUL FOR

Students in introductory physics courses, educators teaching circular motion concepts, and anyone looking to enhance their understanding of dynamics in rotational systems.

jibjab
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Hi everyone, I am taking my first physics class ever and I'm lost! I have a couple of questions that are giving me a lot of trouble. Any assistance you can give me is very much appreciated!

Homework Statement


A turntable rotates counterclockwise at 85 rpm. A speck of dust on the turntable is at (theta)0.31 rad at t=0 s. What is the angle of the speck at t=7.77 s? Answer should be between 0 and 2(pi) rad.

The Attempt at a Solution


For this, I changed 85 rpms to 1.4 rps. I tried to find the angular velocity by dividing 2(pi)rad/1.42 rps, and my answer was 4.42 rad/s. Then I plugged the info into the equation (theta final)=0.31 + (4.42 rad/s)(7.77 s) and got 34.65.
I divided that answer by 2(pi).
I got 5.51 X 2(pi) rad, following the example in the book. I ended up with a final answer of 183 deg, which was wrong.

Homework Statement


The passengers in a roller coaster car feel 58% heavier than their true weight as the car goes through a dip with a 36.1 m radius of curvature. What is the car's speed at the bottom of the dip?

The Attempt at a Solution


I really don't understand how you figure this out without their true weight?

Homework Statement


An Earth satellite moves in a circular orbit at a speed of 5247.66 m/s. What is its orbital period?

The Attempt at a Solution



I used the equation T=2(pi)X(square root)r^3/GM <-- (I hope that makes sense)
using G=6.67 X 10^-11, M=5.98 X 10^24 and r=6.37 X 10^24
My answer was 5057.96 s. I tried a couple other ways but they were wrong too.


Homework Statement


A 182.4 kg block on a 43.1 cm long string swings in a circle on a horizontal, frictionless table at 55 rpm. What is the speed of the block? The tension on the string?

The Attempt at a Solution


This one I just need an equation for, the ones that I've found need either one or the other so I don't know how to go about it?

Thanks in advance for anything you reply to!
 
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For this, I changed 85 rpms to 1.4 rps. I tried to find the angular velocity by dividing 2(pi)rad/1.42 rps, and my answer was 4.42 rad/s.
Shouldn't that be 2(pi)*1.42 rps?

The rest of your calc looks good to me.
 

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