A cyclist starts from rest and pedals so that the wheels make 8.00 revolutions in the first 9.70 s. What is the angular acceleration of the wheels (assumed constant)?

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

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