# Connected Wheels Problem. Angular Velocity.

• EpiphoneBenji
In summary, wheel A of radius 8.9 cm is connected to wheel C of radius 30.7 cm by belt B. At time t = 0 s, wheel A starts rotating at a constant acceleration of 8.6 rad/s^2. We need to find the time at which wheel C reaches a rotational speed of 93.0 rev/min, assuming no slipping occurs. The attempt at a solution involved converting the angular velocity of wheel C to revs/s and dividing by the acceleration, but this does not take into account the difference in time for each wheel to complete one revolution. Additionally, the conversion from angular velocity to linear velocity needs to consider the radius.
EpiphoneBenji

## Homework Statement

Wheel A of radius ra = 8.9 cm is coupled by belt B to wheel C of radius rc = 30.7 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 8.6 rad/s2. At what time will wheel C reach a rotational speed of 93.0 rev/min, assuming the belt does not slip?

## Homework Equations

2 π rad = 1 Rev
v = vo + at ( constant acc)

## The Attempt at a Solution

Wheel A and Wheel C have the same velocity, so I converted the rads to revs and 93 rev/min to 1.55 revs/s and divided the velocity by the acceleration to find the time. But the answer doesn't work. Am I doing something wrong ? Please help !

Thanks

We need to see more of your work to know just were you went wrong. Also, note that the time to for wheel A to complete one revolution is much less than that of wheel B, yet both go through 2$\pi$ radians and your work thus far does not take this difference into account.

But being attached to a string doesn't mean they are going at the same speed ?

Define "speed". Each point on the belt will be be moving at the same rate, but translational velocity and angular velocity are not the same. Your conversion from radians to revs needs to include the fact that angular velocity depends on radius. Try looking up the conversion of tangential velocity to angular on wikipedia.

for providing the problem and your attempt at a solution. It seems like you are on the right track, but there may be a few things that could be causing your answer to be incorrect.

Firstly, it is important to note that the problem states that wheel A starts from rest at t=0. This means that the initial velocity (vo) for wheel A is 0, not the same as wheel C's velocity.

Secondly, when converting from rad/s to revs/s, you need to use the conversion factor of 2π rad = 1 rev, not 1 rad = 1 rev. This will give you a different value for the velocity of wheel C.

Lastly, when using the equation v = vo + at, be sure to use the correct units. In this case, the acceleration is given in rad/s2, so the velocity should be in rad/s as well. This will give you the correct time in seconds.

Using these adjustments, you should be able to solve for the correct time at which wheel C reaches a rotational speed of 93.0 rev/min. Remember to always double check your units and use the correct conversion factors when solving problems like this. Good luck!

## 1. What is the Connected Wheels Problem?

The Connected Wheels Problem, also known as the Bicycle Wheel Problem, is a physics problem that involves two or more wheels that are connected by a common axis. The problem involves determining the relationship between the angular velocities of the connected wheels.

## 2. What is Angular Velocity?

Angular velocity is a measure of the rate of change of angular displacement over time. It is represented by the Greek letter omega (ω) and is measured in radians per second (rad/s). It describes how quickly an object is rotating around an axis.

## 3. How is Angular Velocity related to the Connected Wheels Problem?

In the Connected Wheels Problem, the angular velocities of the connected wheels are related by the ratio of their radii. This means that the ratio of the angular velocities is equal to the ratio of the radii of the wheels. This relationship is known as the law of gearing or the gear ratio equation.

## 4. What are some real-life applications of the Connected Wheels Problem?

The Connected Wheels Problem has many real-life applications, such as in bicycles, gears, and pulley systems. It is also used in engineering and mechanical design to determine the appropriate gear ratios for machines and vehicles.

## 5. How can the Connected Wheels Problem be solved?

To solve the Connected Wheels Problem, you can use the gear ratio equation, which states that the ratio of the angular velocities is equal to the ratio of the radii. You can also use the principle of conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque.

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