Answer:
α=1.07 rad/s²
Explanation:
Given data
Angular displacement ΔS=8.00 revolutions
The time intervals Δt=9.70
To find
Angular acceleration
Solution
In order to find angular acceleration we use following equation
ΔS=ωiΔt+1/2α(Δt)²
As we know the cyclist starts from rest ωi=0 then we got
ΔS=0+1/2α(Δt)²
ΔS=1/2α(Δt)²
Multiply both side by 2÷(Δt)²
So we got
α=2ΔS÷(Δt)²
α={2( 8.00 rev)÷(9.70s)²}×(2π rad÷rev)
α=1.07 rad/s²
The angular acceleration of the wheels will be
[tex]a=1.07 \dfrac{rad}{sec^{2} }[/tex]
Given:-
Time change for the angular displacement=9.70sec,
total revolutions in the time interval Δs= 8rev,
We have to find the angular acceleration of the wheels,
To find out the angular acceleration we need to use the following equation,
[tex]\bigtriangleup S=\omega i\bigtriangleup t+\dfrac{1}{2} a\bigtriangleup t^{2}[/tex]
but as we know that cyclist starts to pedals from the rest hence,
ωi=0
Puting this value in the equation we got,
[tex]\bigtriangleup S=0+\dfrac{1}{2} a\bigtriangleup t^{2}[/tex]
[tex]\bigtriangleup S=\dfrac{1}{2} a\bigtriangleup t^{2}[/tex]
Simplifiying this equation to find the acceleration
[tex]a=2\frac{\bigtriangleup S }{\bigtriangleup T^{2} }[/tex]
[tex]a=2*\dfrac{8}{9.7^2} * 2\pi \frac{rad}{sec}[/tex]
{Here we multiply by 2[tex]\pi[/tex] to convert the answer in rad/sec}
[tex]a=1.07 \dfrac{rad}{sec^{2} }[/tex]
Hence, the angular acceleration of the wheels will be,
[tex]a=1.07 \dfrac{rad}{sec^{2} }[/tex]
To know more about angular acceleration, click the link below,
https://brainly.com/question/408236
