A 1 meter wide door is initially open at an angle of 30o as shown (top view). You push with 20 N force in the middle of the door as shown and the door rotates around the hinge on the left. The door has a rotational inertia =3.0 kg m2. The angular acceleration of the door will be:

angular acceleration = 1.67 rad/s²

Explanation:

given data

door wide = 1 m

initially ope angle = 30°

push force = 20 N

rotational inertia = 3.0 kg m²

solution

we apply force at middle so length will be here r1 =  = 0.5 m

and

now we get here torque that is express as

torque τ = Force × r1 × sin30   ......................1

put her value and we get

torque τ = 20 × 0.5 × sin30

torque τ = 5 Nm

and  we know

torque = rotational inertia × angular acceleration   .......................2

put her value and we get angular acceleration

angular acceleration =  

angular acceleration = 1.67 rad/s²

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.