Moment of Force on a Rigid Body | Engineering Mechanics - Civil Engineering (CE) PDF Download

1.- Kinematics. Types of motion:Translation, Rotation about a fixed axis , General Plane Motion, Motionabout a fixed pint, General Motion

Exercise: Distinguish between curvilinear translation and rotation about a fixed axis

Translation.A motion is said to be a translation if any straight line inside the body keeps the same direction during the movement. All the particles forming the body move along parallel paths. If these paths are straight lines, the motion is said a rectilinear translation; if the paths are curved lines, the motion is a curvilinear motion

Rotation about a fixed axis. The particles forming the rigid body move in parallel planes along circles centered on the same fixed axis. If this axis, called the axis of rotation intersects the rigid body, the particles located on the axis have zero velocity and zero acceleration

General Plane Motion. Any plane motion which is neither a translation or a rotation is referred as a general plane motion. Plan motion is that in which all the particles of the body move in parallel planes. Translation and rotation are plane motions.

Motion about a fixed point. The three-dimensional motion of a rigid body attached at a fixed point, for example, the motion of a top on a rough floor, is known as motion about a fixed point.

General Motion Any motion of a rigid body which does not fall in any of the cathegories above described. 

Exercise: Identify different types of motion

Translation. Motion equations  Fig. 15.1 Fig. 15.7 pag 918

Conclusion: A rigid body in translation can be considered as a particle

will be constant in magnitude (rigid body) and in direction (translation motion), then

the derivative of   is zero

When a rigid body is in translation all the points of the body have the same velocity and the same acceleration.

Rotation about a fixed axis. 

Motion equations. Velocity 

Angular velocity and angular acceleration are invariants. They are the same for all points of the solid. They are a characteristic of the rotating motion of the solid

Exercise: A compact disk rotating at 500 rev/min is scanned by a laser that begins at the inner radius of about 2.4 cm and moves out the edge at 6.0 cm. Which is the linear (tangential) velocity of the disk where the laser beam strikes: (a) at the beginning of scanning and (b) at the end?. The same for acceleration  

Rotation about A Fixed Axis. Motion equations. Acceleration 

Representative slab

Rotation about a Fixed Axis. The Vector Motion Equations

Vector expressions for velocity and acceleration in rotation about a fixed axis

The bucket falls from the rest with a constant linear acceleration of 0.3 g. (a) Estimate the speed of the bucket after 5 seconds and the fallen distance. (b) Compute the angular acceleration of the pulley © How fast will it rotate after 5 s.

Gear 1 rotates clockwise at angular velocity of 12 rad/s. How fast will gear 2 and 3 rotate. Data: R1:5 cm; R2:10 cm; R3:20 cm.

General Plane Motion. Any general plane motion can be considered as a translation plus a rotation

General Plane Motion. Any general plane motion can be considered as a translation plus a rotation

Angular velocity and angular acceleration of rod are independent of the selected point to rotate 

Rolling without slipping.

As the wheel of radius R rotates through angle θ, the point of the contact between the wheel and the plane moves a distance s that is related with θ by s= θ R. 

If there is no sliding, the distance traveled by point C is exactly the same s.

Rolling with slipping. An object slides and rolls

Find the angular velocity of sliding stair of length 3 m, when the velocity of contact point with the soil is 3 m/s. The angles between the stair and the floor is 45º

The slider-crank mechanism converts the rotational motion of crank in linear motion of slider. Find the relationship between the angular velocity of crank and the linear velocity of slider piston