Question

While studying vertical motion imparted to the base of tractor seat, \( \theta \) (radian) is considered as rotation about tractor’s CG and \( R \) is considered as longitudinal distance from operator’s seat to the tractor’s CG. For a small value of \( \theta \), the term ‘\( R\theta \)’ represents the vertical motion resulting from tractor’s _________

• A. pitch motion
• B. roll motion
• C. yaw motion
• D. lateral motion

Hint:

In rotational motion problems, \( R\theta \) typically represents the linear displacement caused by rotational motion, which is often used to model pitch motion for small angles.

Answer 1

The Correct Option is A

In this problem, θ represents the angle of rotation about the tractor's center of gravity (CG), and R is the longitudinal distance from the operator's seat to the tractor's CG. The term Rθ represents the vertical displacement due to the rotational motion of the tractor about its CG.

For small values of θ, this is characteristic of pitch motion, which refers to the up-and-down rotation of the tractor (about the tractor's longitudinal axis). The vertical displacement caused by pitch motion is proportional to the distance from the center of gravity and the angle of rotation.

Thus, the vertical motion is due to the tractor's pitch motion.