Newtonian Mechanics II: Drag Force Centripetal Force

The Drag Force and Terminal Speed: Fluid – anything that can flow (gas or liquid and in some cases, cats. They are weird creatures). Drag Force ( 𝑫 ) – a force that opposes the relative motion and points in the direction in which the fluid flows relative to the body.   Drag Force ( 𝑫 ) – the force exerted by a fluid (air for instance) on the object moving through the fluid. Drag force is dependent on the motion of the object, the properties of the object, and the properties of the fluid that the object is moving through.

The Equation for Drag Force is: C = Drag coefficient ρ = density A = the effective cross-sectional area of the body (The area of a cross- section taken perpendicular to the velocity v .

From the equation, we can see that as the speed of an object increases, so does the magnitude of the drag force.   The size and shape of the object also affects the drag force as you can see from the equation having Area in in it. The drag force is also affected by the properties of the fluid, such as its viscosity and temperature, as represented in the equation by density.

NOTE: Drag force is similar to a frictional force for liquids or gases.   NOTE: If a body falls long enough, the drag force 𝑫 will eventually equal the gravitational force 𝐹 𝑔 . Drag force 𝑫 is an upward force that opposes the downward gravitational force 𝐹 𝑔 on a falling body.

Terminal Speed ( 𝐯 𝐭 ) – when a body falls at a constant speed that means it is no longer accelerating ( 𝑎 =0).

Uniform Circular Motion:   Centripetal acceleration ( 𝑎 𝐶 ) – is the rate of change of a tangential velocity. The direction of the centripetal acceleration is always inwards along the radius vector of the circular motion.

𝐹 𝐶 =𝑚 𝑎 𝐶 NOTE: Because the speed v in uniform circular motion is constant, the magnitudes of the acceleration and the force are also constant. HOWEVER, the directions of the centripetal acceleration and force are not constant; they vary continuously so as to always point toward the center of the circle (that is radially inward).

NOTE: A centripetal force can be a frictional force, gravitational force, or any other force. Basically, it is another force that is causing an object to go in uniform circular motion. For instance, the gravitational force of the Sun causes the planets to rotate around it. NOTE: If a problem is asking for an angle with the vertical concerning uniform circular motion of if it concerns an angle when talking about uniform circular motion then the quick solution is often:   tan θ= v 2 rg