Question

What type of motion is shown by “A point marked on the blade of a running ceiling fan”?

Answer 1

Hint: In order to solve this question, we are going to first analyze the condition of the motion of the ceiling fan, then the point marked on the blades of the ceiling fan is considered and then, we have to see what the motion is like by considering the velocity and the type of movement of the point marked.

Complete answer:
For a point marked on the blade of a ceiling fan, it will be rotating at a constant speed. This gives us two points:
The first one is the circular motion due to the rotation of the blades of the ceiling fan and thus also that of the point marked on the blade.
The second is that the point is not going to leave the blades of the ceiling fan hence, the velocity is not going to change which deduces a uniform motion.
Combining these two facts, we get that the complete motion of the point marked on the blades of the ceiling fan is a uniform circular motion due to constant rotation of the blades of the ceiling fan.

Note: It is important to note that the angular velocity for the motion of the blades is given by the equation:
$$\omega ={\displaystyle \frac{d\theta }{dt}}$$
Where, $$d\theta$$is the angular displacement and $$dt$$is the time taken for it.
Now for the blades of the fan and hence for the point marked, the rate of change of angular displacement is constant.