Question

Calculate the magnitude (in m/s2) of the centripetal acceleration at the tip of a 4.60 m long helicopter blade that rotates at 240 rev/min.

Answer 1

To calculate the centripetal acceleration, convert the blade's rotational speed to rev/s, calculate the linear speed by multiplying the rotational speed with the blade's circumference, and then use the centripetal acceleration formula with the blade's radius.

Step-by-step explanation:

To calculate the magnitude of the centripetal acceleration at the tip of a 4.60 m long helicopter blade that rotates at 240 revolutions per minute (rev/min), we need to use the following formula:

Centripetal acceleration (ac) = (v2) / r

where v is the linear speed of the blade's tip and r is the radius of the blade's rotation.

Firstly, we convert the rotational speed from rev/min to rev/s (since we want our answer in SI units):

240 rev/min = 240 / 60 rev/s = 4 rev/s

Next, the linear speed v can be found by multiplying the rotational speed by the circumference of the circle described by the blade's tip:

v = rotational speed (ω) × circumference


= ω × (2π × r)

Plugging in the values, we get:

v = 4 rev/s × (2 × π × 4.60 m)

v = 4 × 2π × 4.60 m/s

Now, centripetal acceleration can be determined:

ac = (v2) / r

ac = (4 × 2π × 4.60 m/s)2 / 4.60 m

After calculating this expression, we find the centripetal acceleration.