# Find the angular speed at t=3 seconds

• Neon32
In summary, the angular speed of a shaft turning at 65.0 rad/s at time zero is found to be -10 rad/s at t=3 seconds, with a non-constant angular acceleration given by α = -10 rad/s^2 - 5t rad/s^3. This cannot be solved using kinematic equations as the angular acceleration is not constant, and instead requires the use of differential equations with respect to time.
Neon32

## Homework Statement

A shaft is turning at 65.0 rad/s at time zero. Thereafter, its angular acceleration is given by α = -10 rad/s 2 - 5t rad/s 3 where t is the elapsed time. (a) Find its angular speed at t = 3.00 s. (b) How far does it turn in the 3.00 s seconds?

t=3 seconds

## Homework Equations

Wf=Wi+αt where α is the angular acceleration

## The Attempt at a Solution

since α = -10 - 5t (1)
at t= 3 seconds
by substitution in (1):

From Kinematic equation:
wf=wi+αt

Looks like you tried to solve it by using an equation restricted to constant angular acceleration. Is the angular acceleration constant in this problem? You calculated α at t = 3 s, but that's not the angular acceleration at other instants of time between t = 0 and t = 3 s.

Neon32
TSny said:
Looks like you tried to solve it by using an equation restricted to constant angular acceleration. Is the angular acceleration constant in this problem?
Yes it isn't constant. So basically i can't use kinematic equations if the acceleration isn't constant??

Neon32 said:
Yes it isn't constant. So basically i can't use kinematic equations if the acceleration isn't constant??
Yes. You need to use differential equations w.r.t. time.

Neon32
cnh1995 said:
Yes. You need to use differential equations w.r.t. time.

Alright. Thanks both of you for the help. Appreciated :)

## What is angular speed?

Angular speed is a measure of how quickly an object rotates or moves around a fixed point. It is expressed in radians per unit of time, such as radians per second.

## How is angular speed calculated?

Angular speed is calculated by dividing the angle traveled by the time it takes to travel that angle. It can be represented by the formula ω = Δθ/Δt, where ω is the angular speed, Δθ is the change in angle, and Δt is the change in time.

## How is angular speed different from linear speed?

Angular speed is a measure of the rate of change in an object's angle, while linear speed is a measure of the rate of change in an object's position. Angular speed is measured in radians per unit of time, while linear speed is measured in units of distance per unit of time.

## Why is it important to find the angular speed at a specific time?

Finding the angular speed at a specific time allows us to understand the motion of an object at that moment and make predictions about its future motion. It also helps us to calculate other important quantities such as angular acceleration and tangential velocity.

## What factors can affect the angular speed?

The angular speed of an object can be affected by factors such as its mass, distance from the axis of rotation, and any external forces acting on it. Changes in these factors can cause the angular speed to increase, decrease, or remain constant.

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