Question

A certain type of propeller blade can be modeled as a thin uniform bar 2.70 m long and of mass 24.0 kg that is free to rotate about a frictionless axle perpendicular to the bar at its midpoint.

If a technician strikes this blade with a mallet 1.15 m from the center with a 40.0 N force perpendicular to the blade, find the maximum angular acceleration the blade could achieve.

Answer 1

Given that :

massof the uniform bar, m =24 kg

length of the bar, L = 2.7 m

Force applied, F = 40 N

distance, r = 1.15 m

The maximum angular acceleration of the blade could achieve which given as :

using an equation,    torque applied = I

r F = I

where, I = moment of inertia of centre of mass = (1/12) m L²

I = (1/12) (24 kg) (2.7 m)²

I = 14.5 kg.m²

then, we have

(1.15 m) (40 N) = (14.5 kg.m²)

(46 Nm) = (14.5 kg.m²)

= (46 Nm) / (14.5 kg.m²)

= 3.17 rad/s²