Question

A group of students must conduct an experiment to determine how the location of an applied force on a classroom door affects the rotational motion of the door. The rotational inertia of the door about its hinges is known. The initial angular velocity of the door is zero. The students must determine how to test the relationship between a torque exerted on the door and the change in the angular velocity of the door. All frictional forces are considered to be negligible. How should the experiment be conducted to test the relationship between the torque exerted on the door and the change in the door’s angular velocity in a way that minimizes experimental uncertainty?

Answer 1

Explanation:

In order to perform the experiment the relationship between the torque exerted on the door we have to take into consideration the components of the Torque formula.

$\\\\T = F_{t}*d\\F_{t} = m*a_{t}\\T = m * a_{t} *r$ eq (I)

T = Torque

Ft = Tangential force

d,r = distance from the axis of rotation

m = mass

at = tangential acceleration

at = Δv/Δt (eq II)

Δv = difference of tangential velocity

Δv = difference of time

In order to observe the the velocity and acceleration, the force has to be placed into different distances on the door. By using a chart it will be possible to design a proportional relation between the angular acceleration, by consequence the angular velocity, and the same force F applied along the distance d of the door. In results of the experiment the graph should result in the relations described in the eq (I) and eq (II).