3038.45 in radians and
483.52 in revolutions
The angular velocity (ω) of a rotating body is the time (t) rate of change in the angular displacement (θ) of the body. i.e
ω = θ / t; --------------------------(i)
The following are given in the question;
ω = 33.5rad/s
t = 90.7s
Substitute these values into equation (i) as follows;
33.5 = θ / 90.7
Solve for θ;
θ = 33.5 x 90.7
θ = 3038.45 rad
Convert the value of the displacement from radians (rad) to revolutions (rev)
Remember that;
2π rads = 1 rev
=> 3038.45 rads = (3038.45 / 2π) rev
Take π = 3.142
=> 3038.45 rads = (3038.45 / (2 x 3.142)) rev
=> 3038.45 rads = 483.52 revs
Therefore the angular displacement of the tub during a spin of 90.7s is 3038.45 in radians and 483.52 in revolutions
The angular displacement is 3038 rad or 1519/π revolutions.
We know that;
ω =θ/t
ω = angular velocity
θ = angular displacement
t = time taken
Now;
θ = ωt
Substituting the values in the question;
θ = 33.5 rad/s × 90.7 s
θ = 3038 rad
But
1 rev = 2π rad
x rev = 3038 rad
x = 3038 rad × 1 rev/2π rad
x = 1519/π revolutions
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