# Uniform Circular Motion - Finding Linear Speed

In summary, The Bohr model of the hydrogen atom has one electron rotating around its center with a radius of 5.29 * 10^-11 m and a mass of 9.11 * 10^-31. The electrostatic force between the orbiting electron and the center proton is 8.20 * 10^-8. Using the equations t = 2 ∏ r / v and v = √(ra), the centripetal acceleration of the electron was found to be 9.00 * 10^22 and the linear speed to be 2,182,104.645 m/s. However, the period of the electron's rotation and the correct linear speed are still unknown.

## Homework Statement

The Bohr model of the hydrogem atom has one electron rotating around its center.
If it has a radius of 5.29 * 10-11 m. And the mass of the electron is : 9.11 * 10-31. And the electrostatic force between the orbiting electron and the center proton is 8.20 * 10-8.

Find:
1) the centripetal acceleration of the electron
2) The linear speed of the electron
3) the period of the the electrons rotation

t = 2 ∏ r / V

## The Attempt at a Solution

Part 1 I managed to calculated. I got the correct answer of ac = 9.00 * 1022.

I also found that Velocity is equal to 2182104.645 ms/s.

However for the period and the linear speed I am stuck.

For the period I get:
t = 2 ∏ r / V
t = 1.52321 * 10-16

^according to the answer sheet this answer is wrong and should be, 4.82*10-16

For the linear speed I am stuck. What exactly am I finding? I have no idea what to do.
^ the apparent answer is 6.9 x 105

NOTE: Answers may be wrong as this textbook often has incorrect answers.

Thanks!

Part 1 I managed to calculated. I got the correct answer of ac = 9.00 * 1022.

I also found that Velocity is equal to 2182104.645 ms/s.

For the linear speed I am stuck. What exactly am I finding? I have no idea what to do.
^ the apparent answer is 6.9 x 105

I suspect you've used the wrong numbers.

Did you use v= √(ra) ?

## 1. What is uniform circular motion?

Uniform circular motion is a type of motion in which an object moves along a circular path at a constant speed. This means that the object covers the same distance in the same amount of time, resulting in a constant linear speed.

## 2. How is linear speed calculated in uniform circular motion?

Linear speed in uniform circular motion is calculated by dividing the distance traveled along the circular path by the time it takes to complete one full revolution. This can also be calculated by multiplying the radius of the circular path by the angular velocity, which is the rate of change of the angle with respect to time.

## 3. How is uniform circular motion different from non-uniform circular motion?

In uniform circular motion, the speed of the object remains constant while it moves along the circular path. In non-uniform circular motion, the speed changes at different points along the path, resulting in a varying linear speed. This is due to the presence of external forces, such as friction, acting on the object.

## 4. What is the relationship between linear and angular speed in uniform circular motion?

The relationship between linear and angular speed in uniform circular motion is directly proportional. This means that if the angular speed increases, the linear speed also increases, and vice versa. This relationship is described by the equation v = rω, where v is the linear speed, r is the radius of the circular path, and ω is the angular velocity.

## 5. What are some real-life examples of uniform circular motion?

Some examples of uniform circular motion in everyday life include the motion of a Ferris wheel, a car driving around a roundabout, a record player spinning a vinyl record, and a satellite orbiting the Earth. These objects all move along circular paths at a constant speed, resulting in a constant linear speed.

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