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 understand some basic concepts related to circular motion, such as the circumference of a circle and the relationship between angular velocity and linear velocity.
(a) The distance the point moves in one revolution is equal to the circumference of the circle formed by the path of the point. The circumference of a circle can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.
In this case, the radius is given as 0.11 m. So, the distance the point moves in one revolution is C = 2π(0.11) = 0.22π m.
(b) The speed of the point can be calculated by multiplying the distance moved in one revolution by the number of revolutions per unit time. In this case, the fan completes 1200 revolutions every minute. To convert this to seconds, we divide by 60 (since there are 60 seconds in a minute). So, the speed of the point is v = (0.22π m/rev) * (1200 rev/60 s) = (0.22π * 20) m/s.
(c) The magnitude of the acceleration can be calculated using the formula: a = v^2 / r, where a is the acceleration, v is the speed, and r is the radius.
Using the speed calculated in part (b) and the given radius of 0.11 m, we can calculate the magnitude of the acceleration as a = (0.22π * 20)^2 / 0.11 m/s^2.
(d) The period of motion is the time taken for one complete revolution. It can be calculated using the formula: T = 1/f, where T is the period and f is the frequency. In this case, the frequency is given as 1200 revolutions per minute. To convert this to seconds, we divide by 60. So, the period is T = 1 / (1200 rev/60 s) = 60/1200 s.
Now, you can substitute the given values into the equations to find the numerical answers.