Question

In the space, explain how this motion was different from when the mass was attached to your foot? Make special note of angular displacement, angular velocity, angular acceleration, and the amount of effort you put into this motion.

Answer 1

Answer:

Explanation:

To make the body to rotate about its axis , torque is required . The relation for torque in mechanics is  τ = I α         1

where τ is the torque , I is the moment of inertia of the body and α is the angular acceleration.

The moment of inertia I = m r²  ; m is the mass of body and r is the distance from the axis of rotation . In this case we have attached the mass to the foot . By which its moment of inertia increases . We have not applied any torque , that means the torque will remain the same

In equation 1 If I increases , the value of α will decrease because torque is constant . Thus angular acceleration will decrease .

The angular displacement θ = ω₀ t + 1/2 α t²

where ω₀ is the initial angular velocity and α is the angular acceleration .

As the α decreases the value of θ also  decreases .

The angular displacement can be defined as the angle described by the rotating body in one sec .

Similarly ω = ω₀ + α t

This also depends upon angular acceleration , which decreases .

That means angular velocity also decreases .

As no torque is required in this case , because in space , there is no force of friction .

Thus the work done  W = τθ will be equal to zero , because τ is zero