Torque about the axis passing through the center of the circle.

Question

A 0.75 kg airplane is attached by an arm rod of negligible mass flies in horizontal circle 1.5 m in radius. The airplane model acts a force of 0.8N perpendicular to the rod. By assuming the airplane as a point mass, calculate

(i) Torque about the axis passing through the center of the circle.
(ii) Angular acceleration of the airplane.
(iii) Linear acceleration of the airplane tangent to its flight path.

Answer 1

(i)

 

If the applied force is perpendicular to the radius, then the torque is

 

τ = rF = (1.5 m)(0.8 N) = ?

 

(ii)

 

Use the relation

 

τ = Iα ⇒

 

α = τ/I

 

I = mr² = (0.75 kg)(1.5 m)² = ? kg m²

 

Plug this value of I and the torque from part (i) into the equation for α, and get an answer in units of rad/s².

 

(iii)

 

See Comment below for the answer to this part. I am having trouble editing in this window.