# Angular velocity and acceleration

• enger
In summary, the problem involves a fixed spring attached to a vertical circular smooth tube and a slider with a mass m that can slide smoothly along the tube. The goal is to find the angular velocity, angular acceleration at any angle, and the angle at which the slider comes to rest. The equations used are conservation of energy and Newton's second law. The attempted solution includes the forces fn and ft, where ft does not take into account the spring's force directed towards the circle's centre. A mistake may have been made and further assistance is needed.
enger

## Homework Statement

the spring oa is fixed from one end o to the bottom of a vertical circular smooth tube and from its other end to a slider a of mass m which can slide smoothly along the tube initially started from rest at a .
find :
i) angular velocity
II) angular acceleration at any angle
iii)angle at which the slider comes to instantaneous rest

## Homework Equations

Conservation of energy and netwen 2nd law

1/2 mv^2 + 1/2 Kx^2 + mgh=1/2 mv^2 + 1/2 Kx^2 + mgh

## The Attempt at a Solution

fn=fan = mrΘdot = n-mgcosΘ +kx
ft=f at = mrΘt double dot = -mgsinΘ

Θ(dot)^2 = 2mgcosΘ + 2gr

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i think i made a mistake & hope someone can help with this situation

I'd like to see your working for your attempted solution. The fact that you have kx appearing in your expression for fn but not adding a component to ft suggests that you are viewing the spring's force as directed towards the circle's centre. It isn't.

## 1. What is angular velocity?

Angular velocity is the rate of change of angular displacement with respect to time. It is a vector quantity that expresses the rotational speed and direction of an object.

## 2. How is angular velocity measured?

Angular velocity is typically measured in radians per second (rad/s) or degrees per second (deg/s). It can be calculated by dividing the change in angular displacement by the change in time.

## 3. What is the relationship between angular velocity and linear velocity?

Angular velocity and linear velocity are related through the radius of rotation. The linear velocity is equal to the angular velocity multiplied by the radius of rotation. This means that objects with a larger radius will have a greater linear velocity for the same angular velocity.

## 4. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity with respect to time. It is a vector quantity that expresses the change in rotational speed and direction of an object.

## 5. How is angular acceleration related to torque?

Angular acceleration and torque are directly proportional to each other, according to Newton's second law for rotational motion. The greater the torque applied to an object, the greater its angular acceleration will be.

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