How long does it take for a wheel rotating with an angular velocity of 5 rad / s to make 150 revolutions?
| August 13, 2021 | education
w = 5 rad / s.
n = 150.
t -?
The angular speed of rotation w shows the angle φ the wheel turns per unit of time t: w = φ / t.
The angular velocity w = 5 rad / s means that the wheels turn through the angle φ1 = 5 rad in t1 = 1 s.
One complete revolution is the angle φ (1) = 2 * P radians.
The time of one complete revolution will be t (1) = φ (1) / w = 2 * P rad / 5 rad / s = 1.256 s.
We have such revolutions n = 150, so we will find the time of these revolutions by the formula: t = n * t (1).
t = 150 * 1.256 s = 188.4 s.
Answer: the wheel will make 150 revolutions in a time t = 188.4 s.
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