Projectiles launced horizontally

The key for the analysis is to break the motion into the vertical component and horizontal component.

?y = v_iyt + 1/2 a_yt² = 1/2 gt², because v_iy=0 and a_y = g

?x = v_ixt + 1/2 a_xt² = v_ixt, because a_x = 0

Projectiles launced at an angle

The key for the analysis is to break the motion into the vertical component and horizontal component.

v_ix = v cos? and v_iy = v sin?

V_y = v_iy + at

v_iy - gt_up = 0

t_up = v_iy/g

?y = v_iyt + 1/2 at²

?y_max = v_iyt_up - 1/2 g(t_up)² = 1/2 (v_iy²/g)

Uniform circular motion

The direction of the acceleration (the centripetal acceleration) is toward the center of the circule and its magnitude is a_c = v² / r, where v is velocity and r is radius of the circle.

For uniform circular motion: magnitude of velocity v = 2?r / T, where r is radius and T is period (in seconds).

Period T = 1/f, where f is frequency.

a_c = 4?²r / T², where r is radius and T is period.

?

All objects resist changes in their state of motion. All objects have inertia.

The tendency of an object to resist changes in its state of motion varies with mass.

The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion.

Suppose that there are two seemingly identical bricks at rest. Yet one brick consists of mortar and the other brick consists of Styrofoam. Without lifting the bricks, you could give the bricks an identical push in an effort to change their state of motion. The brick that offers the least resistance is the brick with the least inertia - and therefore the brick with the least mass (i.e., the Styrofoam brick).

Also known as Newton's first law of motion, the law of inertia states that:

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction (ie, same velocity) unless acted upon by an unbalanced force.

Inertia is the tendency of an object to resist changes in its velocity. 

Newton's third law is: For every action, there is an equal and opposite reaction.

A force is a push or a pull that acts upon an object as a results of its interaction with another object. Forces result from interactions! Some forces result from contact interactions and other forces are the result of action-at-a-distance interactions.

According to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body. There are two forces resulting from this interaction - a force on the chair and a force on your body. These two forces are called action and reaction forces and are the subject of Newton's third law of motion.

Newton's second law of motion can be formally stated as follows:

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This verbal statement can be expressed in equation form as follows:

The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration.

Work

When a force is applied to an object over a displacement, work is done to the object. Work is transfer of energy.

W = F * d * cos Ɵ

Work is measured in joule and is a scalar, 1 joule = 1 Newton meter  More...

Linear Momentum

(Linear) Momentum is a measurement of mass in motion: how much mass is in how much motion. It is usually given the symbol p.

By definition, p = m * v

Where m is the mass and v is the velocity. The standard units for momentum are kg⋅m/s, and momentum is always a vector quantity.  More...

Uniform circular motion

In uniform circular motion, the direction of the acceleration (the centripetal acceleration) is toward the center of the circule and its magnitude is a_c = v² / r, where v is velocity and r is radius of the circle.

In uniform circular motion: magnitude of velocity v = 2Πr / T, where r is radius and T is period (in seconds). Period T = 1/f, where f is frequency.

a_c = 4Π²r / T², where r is radius and T is period.  More...

Cycle, Period, Amplitude, Frequency, Wavelength

Cycle: One complete repeat of the pattern/vibration

Period: The time required to complete one cycle. (unit is s)

Amplitude: The distance from the equilibrium position (resting position) to the maximum displacement when in motion.

Frequency: the reciprocal of period (unit is Hz: 1 Hz = 1 s ^-1).

Wavelength: the length of one complete wave cycle.

Simple Harmonic Motion

Simple harmonic motion is any periodic motion in which:

• The acceleration of the object is directly proportional to  its displacement from its equilibrium position.
• The acceleration is always directed towards the equilibrium position.

2 examples of simple harmonic motion are the spring and the pendulum.  More...

Newton's Law of Universal Gravitation

F_g = GM₁M₂ / R²

Since F_g = m * a, we have

a = F_g / m = GM_e / Re²

Where M_e is earth's mass, and Re is radius of earth in meters.  More...