In one line
General plane motion is the combination of translation and rotation of a rigid body in a plane, like a rolling wheel or a connecting rod.
Explained simply
A book sliding across a table without turning is in translation. A ceiling fan blade spinning about its fixed axle is in rotation. A rolling bicycle wheel both moves forward and spins: that is general plane motion.
Technically, a rigid body is in plane motion when all its particles move in parallel planes. Three types: (1) translation (every line in the body stays parallel to itself; rectilinear or curvilinear), (2) rotation about a fixed axis, (3) general plane motion = translation + rotation.
How it works
- In translation, all points have the same velocity and acceleration at an instant.
- In fixed-axis rotation, each point moves in a circle: \( v = r\omega \), \( a_t = r\alpha \), \( a_n = r\omega^2 \).
- In general plane motion, the whole body has one angular velocity \( \omega \), but points have different velocities.
- The motion can be seen as translation with a reference point plus rotation about that point.
- A neat shortcut: at any instant, the motion is pure rotation about one point with zero velocity, the instantaneous centre of rotation (ICR).
Key formula
Fixed-axis rotation: \( v = r\omega \) (m/s), \( \omega \) in rad/s, \( \omega = 2\pi N/60 \) for N in rpm.
Quick example
In an engine: the piston translates, the crank rotates about a fixed axis, and the connecting rod has general plane motion. A wheel rotating at 300 rpm has \( \omega = 2\pi(300)/60 = 31.4 \) rad/s.
Common mistakes
- Calling a Ferris-wheel seat (that stays upright) 'rotation'; it is curvilinear translation.
- Assuming all points of a body in general plane motion have the same velocity.
- Using rpm directly in \( v = r\omega \) without converting to rad/s.
How MU asks it
A 3-mark theory part: 'Explain the types of rigid body motion with examples' or 'Define general plane motion'. Give definitions with one sketch and example each. It sets up the ICR numericals.