Question

A fan is rotating at a constant 360.0 rev/min. What is the magnitude of the acceleration of a point on one of its blades 10.0 cm from the axis of rotation?

a) 0.0 m/s²
b) 6.28 m/s²
c) 62.8 m/s²
d) 628 m/s²

Answer 1

The magnitude of the acceleration of a point on the fan blade, located 10.0 cm from the axis of rotation, is approximately 62.8 m/s².

Step-by-step explanation:

To calculate the magnitude of the acceleration of a point on the fan blade, we need to use the formula for centripetal acceleration:

centripetal acceleration = (angular velocity)^2 * radius

Given that the fan is rotating at a constant 360.0 rev/min, the angular velocity can be calculated as:

angular velocity = (360.0 rev/min) * (2π rad/rev) / (60 s/min)

Substituting the values into the formula, we get:

centripetal acceleration = ((360.0 rev/min) * (2π rad/rev) / (60 s/min))^2 * 10.0 cm

Calculating the expression, the magnitude of the acceleration comes out to be approximately 62.8 m/s². Therefore, the correct answer is option c) 62.8 m/s².