A rotating fan completes 1200 revolutions every minute. Consider a point on the tip of a blade, at a radius of 0.11 m.
(a) Through what distance does the point move in one revolution?
m
(b) What is the speed of the point?
m/s
(c) What is the magnitude of its acceleration?
m/s2
(d) What is the period of the motion?
s
To answer these questions, we need to use some basic formulas related to circular motion. Let's go step by step:
(a) To calculate the distance covered by the point in one revolution, we can use the formula:
Distance = Circumference of the circle = 2πr
where r is the radius of the circle. In this case, the radius is given as 0.11 m. So we have:
Distance = 2π * 0.11 = 0.69 m
Therefore, the point on the tip of the blade moves a distance of 0.69 meters in one revolution.
(b) The speed of the point can be calculated using the formula:
Speed = Distance / Time
In this case, the time taken for one revolution is given as 1 minute. But we need to convert it to seconds, so:
Time = 1 minute * 60 seconds/minute = 60 seconds
Now we can calculate the speed:
Speed = 0.69 m / 60 s ≈ 0.012 m/s
Therefore, the speed of the point is approximately 0.012 m/s.
(c) The magnitude of acceleration for circular motion can be calculated using the formula:
Acceleration = (Speed)² / Radius
In this case, we already know the speed from part (b) and the radius is given as 0.11 m. So we have:
Acceleration = (0.012 m/s)² / 0.11 m ≈ 0.0013 m/s²
Therefore, the magnitude of the acceleration is approximately 0.0013 m/s².
(d) The period of motion is the time taken for one complete cycle. Since we already know the time taken for one revolution is 60 seconds, the period of motion is also 60 seconds.
Therefore, the period of the motion is 60 seconds.
So, to summarize:
(a) The point moves a distance of 0.69 meters in one revolution.
(b) The speed of the point is approximately 0.012 m/s.
(c) The magnitude of its acceleration is approximately 0.0013 m/s².
(d) The period of the motion is 60 seconds.