Question

You are a farmer and you come to a gate in your fence. The gate is 35 kg, 3 m long and rotates about one end. You can model it as a thin rod rotating about one end. What is the moment of inertia of the gate as you push it (in kgm2)?

You are a farmer and you come to a gate in your fence. You apply a force of 50 N perpendicular to the length of the gate at the end opposite to the hinges (3 m from the hinges). When you push on the gate, what is its angular acceleration (rad/s2)?

Answer 1

Here we have given that,

Mass of the gate is 35 kg,

Length of the gate is 3 m long

Axis of rotation is about one end.

Now for considering it as a thin rod rotating about one end.

Then for the moment of inertia of the gate as you push it

Here as we know that the moment of inertia of a thin rod rotating about one of its axis is given as

I = 1/3 × M L^2 = 1/3 × 35 × 3^2 = 105 kgm2

Now for the next question,

Here we have given that,

applied force = 50 N

At 3 m from the hinges.

Now When we push on the gate,

its angular acceleration is given as,

Here the torque is T = 50 ×3 =150 Nm

I = 105 kgm²

a = 150/105= 1.42857 rad/s²

Now the angular acceleration si given as,

a = T/I = 1.42857 rad/s²