Newton's First Law — Question 5

Question 5

A steadily translating laboratory is also an inertial candidate

In inertial laboratory L a free body has $x=8+6t$ m. Frame S has origin $X=2+4t$ m and parallel axes. Use numerical seconds.

1. Find its motion in S.

2. Does it satisfy the first law in both frames?

3. Choose a constant frame velocity that makes the body stationary and explain why this changes no interaction.

Question 5 - Solution

A steadily translating laboratory is also an inertial candidate

(a) Subtract the moving origin.

$$x_S=x_L-X=6+2t,\quad \boxed{v_S=2\,\mathrm{m/s},\quad a_S=0}$$ $x_S=6+2t$ m, so $v_S=2$ m/s and $a_S=0$.

(b) Compare accelerations.

$$a_S=a_L-\ddot X=0-0=0$$ Both descriptions have zero acceleration. Constant relative translation preserves the first-law free-particle test.

(c) Move with the body.

$$v'=v_L-U=6-U=0\ \Rightarrow\ U=6\,\mathrm{m/s}$$ An origin moving at 6 m/s in L makes the body’s velocity zero. Its position may remain a nonzero constant if the initial origins differ. The coordinate choice changes the measured velocity, not the physical forces.