# Curvilinear Translation (Projectile Motion)

Projectile motion follows a parabolic trajectory. The vertical component of projectile is under constant gravitational acceleration and the horizontal component is at constant velocity. For easy handling, resolve the motion into x and y components and use the formulas in rectilinear translation.

Form the figure below:

$v_{oy} = v_o \, \sin \theta$

# Kinematics

**Motion of a Particle**

Particle is a term used to denote an object of point size. A system of particles which formed into appreciable size is termed as body. These terms may apply equally to the same object. The earth for example may be assumed as a particle in comparison with its orbit, whereas to an observer on the earth, it is a body with appreciable size. In general, a particle is an object whose size is so small in comparison to the size of its path.

**Rectilinear Translation (Motion Along a Straight Line)**

# Dynamics

**Dynamics** is the branch of mechanics which deals with the study of bodies in motion.

**Branches of Dynamics**

Dynamics is divided into two branches called *kinematics* and *kinetics*.

Kinematics is the geometry in motion. This term is used to define the motion of a particle or body without consideration of the forces causing the motion.

Kinetics is the branch of mechanics that relates the force acting on a body to its mass and acceleration.

**Symbols and Notations**

s = distance

# 820 Unsymmetrical I-section | Moment of Inertia

**Problem 820**

Determine the moment of inertia of the area shown in Fig. P-819 with respect to its centroidal axes.

# 819 Inverted T-section | Moment of Inertia

**Problem 819**

Determine the moment of inertia of the T-section shown in Fig. P-819 with respect to its centroidal X_{o} axis.

# 818 Hollow square section | Moment of Inertia and Radius of Gyration

**Problem 818**

A hollow square cross section consists of an 8 in. by 8 in. square from which is subtracted a concentrically placed square 4 in. by 4 in. Find the polar moment of inertia and the polar radius of gyration with respect to a z axis passing through one of the outside corners.

# 817 Hollow Tube | Moment of Inertia and Radius of Gyration

**Problem 817**

Determine the moment of inertia and radius of gyration with respect to a polar centroidal axis of the cross section of a hollow tube whose outside diameter is 6 in. and inside diameter is 4 in.

# 816 Polar moment of inertia and radius of gyration at one corner of rectangle

**Problem 816**

A rectangle is 3 in. by 6 in. Determine the polar moment of inertia and the radius of gyration with respect to a polar axis through one corner.

# Moment of Inertia and Radius of Gyration

**Moment of Inertia**

Moment of inertia, also called the second moment of area, is the product of area and the square of its moment arm about a reference axis.

Moment of inertia about the x-axis: