a wheel is making 300rev/min about its center, calculate the angular velocity of any point on the wheel about the center. also find the speed of a point at a distance of 2cm from the center.
A. Va=300rev/min*6.28rad/rev*(1min/60s) =31.4 rad/s.
B. C = p1*2r = 3.14*4cm = 12.56 cm =
Circumference.
V = 300rev/min*12.56cm/rev*(1min/60s) =
62.8 cm/s. = 0.628 m/s.
To find the angular velocity of any point on the wheel about the center, we can use the formula:
Angular velocity (ω) = 2πf
Where f is the frequency, which can be calculated by dividing the number of revolutions per minute (RPM) by 60 seconds:
f = 300 RPM / 60 s = 5 Hz
Now, substituting the value of f into the formula, we get:
ω = 2π * 5 Hz = 10π rad/s (angular velocity)
To find the speed of a point at a distance of 2 cm from the center, we use the formula:
Speed (v) = ω * radius
The radius is given as 2 cm, so substituting the values, we have:
v = 10π rad/s * 2 cm = 20π cm/s
Thus, the speed of the point at a distance of 2 cm from the center is 20π cm/s.