circular motion is best analyzed in a coordinate system with

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Circular Motion

Circular Motion

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movie movie movie Interface Motion detector Force sensor software file software file Dynamics track Pulley Hanging masses

Introduction

It is quite common for objects to move along circular or semi-circular paths. Although these motions can be analyzed using a traditional xy-coordinate system, other coordinate systems, such as polar coordinates, and other sets of kinematic variables (angular variables rather than linear variables) are quite useful. In this activity, the relationships between x- and y-position and velocity to radial and tangential position and velocity, as well as angular position and velocity, will be explored.

I. Circular Motion

Open and select Insert/Movie. Find the movie and open it. Play the movie.

The movie shows a piece of tape with five equally-spaced dots attached to a rotating platform. The central dot is at the center of the platform. Return the movie to the first frame.

Extract position vs. time data for the outermost dot. This dot is 12 cm from the center of the platform. Scale the movie, move your coordinate system to the center of the platform, and rotate your coordinate system so that the initial angular position of the dot is zero.

A. X-Position, Y-Position and Radial Position

Create a graph of x- and y-position vs. time.

Using Data/New Calculated Column, create a new column for the radial position (the position in polar coordinates) of the dot. Add the radial position to your graph of x- and y-position vs. time and print and attach your graph to the end of the activity.

Question: Describe your graph. Do the x, y, and radial positions look as you expect?B. X-Velocity, Y-Velocity, and Tangential Velocity

Create a graph of x- and y-velocity vs. time. Using Data/New Calculated Column, create a new column for the tangential velocity (the velocity in polar coordinates) of the dot. Add the tangential velocity to your graph and print and attach your graph to the end of the activity.

Question: Describe your graph. Do the x, y, and tangential velocities look as you expect?C. X- Position, X-Velocity, and X-Acceleration

Create a graph of x-position, x-velocity, and x-acceleration vs. time. (Use Data/New Calculated Column, to create x-acceleration.) Print and attach your graph to the end of the activity.

Question: Describe your graph. Do the x-position, x-velocity, and x-acceleration look as you expect?D. Angular Position, Angular Velocity, and Angular Acceleration

Create a graph of angular position, angular velocity, and angular acceleration vs. time. (You must first create these columns.) Print and attach your graph to the end of the activity.

Question: Describe your graph. Do the angular position, angular velocity, and angular acceleration look as you expect?E. Circular Motion with Different Radius

Extract additional position vs. time data, this time for the dot 6 cm from the center.

Question: Carefully explain how the x- and y-position data for the dot 6 cm from the center compares to the same data for the dot 12 cm from the center.Question: Carefully explain how the x- and y-velocity data for the dot 6 cm from the center compares to the same data for the dot 12 cm from the center.Question: Carefully explain how the angular kinematic data for the dot 6 cm from the center compares to the same data for the dot 12 cm from the center. II. Force and Circular Motion

Open the file

Set the force sensor to the ±10 N setting, and calibrate the force sensor with a 200 g mass.

Create a pendulum by attaching a string to the force sensor, passing the string over a pulley, and attaching a 200 g mass to the end of the string. Adjust the endstop of the track to hold the force sensor at rest. You should be able to oscillate the mass back and forth without the force sensor moving. Orient a motion detector to measure the position of the oscillating mass.

Collect data for one complete cycle of the motion. Create graphs of position, velocity, and force vs. time. Print these graphs on the same page. With a vertical line, designate the time(s) at which the mass passes through the equilibrium position.

Question: Clearly explain why the force exerted by the string on the mass is greater than the weight of the mass when the mass passes through equilibrium.Question: Clearly explain why the force exerted by the string on the mass is less than the weight of the mass when the mass momentarily stops at each end of its swing.Question: Draw a free-body diagram for the mass as it passes through equilibrium, apply Newton’s Second Law, and calculate the theoretical value for the force exerted by the string. Compare this value to the value measured by the force probe. Comment on the agreement between these two values.Question: Draw a free-body diagram for the mass as it momentarily stops at the end of one swing, apply Newton’s Second Law, and calculate the theoretical value for the force exerted by the string. Compare this value to the value measured by the force probe. Comment on the agreement between these two values.

Source : courses.lumenlearning.com

Chapter 8, 9, 10 Flashcards

Study with Quizlet and memorize flashcards terms like When drag is included, the launch angle of a projectile which maximizes the range is, Circular motion is best analyzed in a coordinate system with, For uniform circular motion, the net force and more.

Chapter 8, 9, 10

When drag is included, the launch angle of a

projectile which maximizes the range is

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Less than 45

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Circular motion is best analyzed in a coordinate

system with

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r-, t-, and z-axes.

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1/52 Created by rachael_griffin7

Terms in this set (52)

When drag is included, the launch angle of a

projectile which maximizes the range is

Less than 45

Circular motion is best analyzed in a coordinate

system with r-, t-, and z-axes.

For uniform circular motion, the net force

Points toward the center of the circle.

The centrifugal force and centripetal force

Is a fictitious force.

Newton's 2 law x com

A=f/m

Newton's 2nd law y com

A=f-mg/m Range

the distance it travels before

it returns to the same elevation from which it was launched. The maximum range occurs for 45.

Range equation

r=[ v ۪² ∙ sin(2ø)]/g

Projectile motion

When drag is included, the angle for maximum range of a projectile depends both on its size and mass.

The r-axis net force

(radial) points from the particle toward the center of the circle.

The t-axis

(tangential) is tangent to the circle, pointing in the ccw direction.

The z-axis

is perpendicular to the plane of motion

static friction

a friction force that acts on objects that are not moving. Prevents car from slipping up hill at higher speeds and down hill at lower speeds.

circular orbital motion

If v is small then particle falls to the ground along parabolic trajectory.

orbit (v)

(v) when one object travels in a circle around another object. Large v.

Spherical planet

Gravity point towards center.

fictitious force

a force having no physical origin. Not real force.

centrifugal force

the outward force on a body moving in a curved path around another body

Two coins on a turntable. Speeding up. Which flies off first?

Coin closest to the edge.

loop the loop

Not uniform circular motion. Slows down going up, speeds up going down.

Acceleration is centripetal

At top and bottom points of the loop.

Bottom

Feel heavy. Fn is larger at bottom. +mg

Top Feel lighter. -mg

Critical speed for loop-the-loop

The speed when n=0. Slowest speed car can complete the circle w/out falling off the track.

Momentum

A quantity defined as the product of the mass and velocity of an object

impulse

Large force, Short duration of force, area under force vs time curve.

Total momentum is conserved

If system is isolated

inelastic collision

Objects stick together, momentum is conserved, but some kinetic energy is lost

Impulse momentum theorem

states that the impulse acting on an object is equal to the change in the momentum of the object

Light cart and heavy cart, same force, same time. Momentum is

Equal. Same force, same time= same impulse. Same impulse= same change momentum.

Throwing ball at door, which ball?

Super all bc larger change momentum so more impulse to door.

conservation law

Some of momenta before and after collisions are equal.

Rate of change of total momentum of a system

Is equal to the total net force applied to the system.

Mosquito and truck. Larger change of momentum?

Same. Equal but opposite.

perfectly inelastic collision

Two objects stick together and move together with common velocity, energy is dissipated inside object as thermal E.

explosion

Internal forces, brief intense interaction then move apart.

Kinetic Energy (KE) Energy of motion potential energy

stored energy that results from the position or shape of an object

thermal energy

The total energy of motion in the particles of a substance

Law of conservation of energy

The transfer of one type of energy to another type of energy.

Work

Transfer of energy from one system to another via forces.

K + Ug

Always constant and equal

Same height Same velocity K constant

Spring constant, slope of hooks law

Elastic potential energy

... Restoring force

Hooks law, displacement from equilibrium and force produced by spring, s

bc change in (s)^2

Us is always positive if spring is stretched or compressed.

Stable equilibrium

Small disturbances causing small oscillating

Unstable equilibrium

Small disturbances cause particle to move away.

Energy particle with downward slope

Speeding up, loosing potential energy, gaining kinetic energy

Particle turning point

The meters where the slope crosses the TE line

Perfectly elastic collision

Mechanical energy is conserved.

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Source : quizlet.com

describe the coordinate system that is usually chosen for analyzing circular motion and state at

Describe the coordinate system that is usually chosen for analyzing circular motion and state at least one advantages for this choice. - 9334691

03/25/2018 Physics College

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describe the coordinate system that is usually chosen for analyzing circular motion and state at least one advantages for this choice.

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