# Analyzing Angular Motion of a Ferris Wheel

• firezap
In summary, the conversation discussed a problem involving a ferris wheel with an angular acceleration of 0.040 rad/s^2. The goal was to find the velocity of a rider at a certain point on the wheel, the radial and tangential components of their acceleration, and how much farther the wheel must turn for the rider to reach a speed of 6.00m/s. The relevant equations were v = ωr, a = (ωF - ωI)/t, and a = ω^2r. Ultimately, the solutions were found by using the formulas v = √2atheta x r and a = √2(0.04)(∏/2) x 15.
firezap

## Homework Statement

Starting from rest, a ferris wheel of diameter 30.0m undergoes an angular acceleration of 0.040 rad/s^2. A certain rider is at the lowest point of the wheel just as it starts to move.
a)find the velocity of the rider just as he completes a quarter of a turn.
b)find the radial and tangential components of his acceleration at the same point.
c)how much farther must the wheel turn before the rider attains a speed of 6.00m/s(the maximum that occurs during the ride)?

## Homework Equations

v = ωr
what other equations?

## The Attempt at a Solution

circumference of ferris wheel is 94.2m and a quarter of that is 23.56m. 2pi is a circle and a quarter of that is pi/2. I have no idea how to do this. the answers from the back are
a)5.32m/s up
b)0.600m/s^2up and 1.88m/s^2 toward center
c)24.6 degrees

firezap said:

## Homework Equations

v = ωr
what other equations?
Three more spring to mind.
Are you familiar with a kinematic equation relating distance, acceleration and initial and final speeds (that's valid when acceleration is constant)? There is a completely analogous formula for angular movement.
There is a formula relating angular acceleration to tangential acceleration (for constant radius) very similar to the one you quote for velocities.
You will also need a formula for centripetal acceleration.

yes. a = (ωF - ωI)/t . i don't know time

#### Attachments

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You may not have been given time, but you have been given theta.

firezap said:
yes. a = (ωF - ωI)/t . i don't know time
Those equations each involve four out of the same five variables. Of those five, which three do you know and which do you want to find? Which equation does that mean you should use?

ty i got it v = √2atheta x r = √2(0.04)(∏/2) x 15
what do i do for question b and c

never mind i know how to do question b. need help on question c

never mind i figured it out ty bye

## 1. What is angular motion?

Angular motion refers to the movement of an object around a fixed point or axis. In the case of a ferris wheel, the wheel rotates around a central axis point, causing the cabins to move in a circular motion.

## 2. How does a ferris wheel use angular motion?

A ferris wheel uses angular motion through the rotation of the wheel around a central axis point. This motion causes the cabins to move in a circular path, providing riders with a scenic view from different heights.

## 3. What factors affect the angular motion of a ferris wheel?

The angular motion of a ferris wheel can be affected by various factors such as the size and weight of the wheel, the speed at which it rotates, and external forces such as wind or friction.

## 4. How does the velocity of a ferris wheel change during its motion?

During its motion, the velocity of a ferris wheel changes constantly. As the wheel rotates, the cabins move at a faster velocity when they are at the top of the wheel and slower when they are at the bottom. This change in velocity is due to the changing distance from the central axis point.

## 5. What is the difference between linear and angular motion?

The main difference between linear and angular motion is the direction of movement. Linear motion refers to movement in a straight line, while angular motion refers to movement around a fixed point or axis. In a ferris wheel, the cabins move in a circular path, making it an example of angular motion.

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