Question

An automatic dryer spins wet clothes at an angular speed of 5.8 rad/s. Starting from rest, the dryer reaches its operating speed with an average angular acceleration of 3.3 rad/s². How long does it take the dryer to come up to speed?

Answer 1

1.7575 seconds

Step-by-step explanation

to solve this we need to use the formula

`\begin{gathered} \omega_f=\omega_i+\alpha t \\ where \\ \omega_f\text{ is the final angular speed} \\ \omega_i\text{ is the initial angular speed} \\ \alpha\text{ is the angular acceleration} \\ t\text{ is the time} \end{gathered}`

Step 1

a)let

`\begin{gathered} initial\text{ angular speed= 0\lparen rest\rparen} \\ final\text{ angular speed=5.8}(rad)/(s) \\ angular\text{ acceleration=}\alpha=3.3(rad)/(s^2) \end{gathered}`

b) now, replace in the formula and solve for t ( time)

`\begin{gathered} \omega_(f)=\omega_(i)+\alpha t \\ 0(rad)/(s)=5.8(rad)/(s)+3.3(rad)/(s^2)*t \\ 0=5.8+3.3t \\ subtract\text{ 5.8 in both sides} \\ 0-5.8=5.8+3.3t-5.8 \\ -5.8=3.3t \\ divide\text{ both sides by 3.3} \\ (-5.8)/(3.3)=(3.3t)/(3.3) \\ t=1.7575 \\ (\text{ the negative sign indicates the acceleration is negative, opposite to motion way\rparen} \end{gathered}`

therefore, the answer is

1.7575 seconds