Reference Frames

We choose the x-y-z axis relative to another object.

What reference frame you choose can affect kinematic variables.

Book on a moving car - the book is moving relative to the road but not the car.

Generalized: $$V_{o2} = V_{o1} + V_{12}$$

$$V_{br} = V_{bc} + V_{cr}$$

Velocity of the book with respect to the road is equal to the velocity of the book with respect to the car plus the velocity of the car with respect to the road.

Dynamics

The causes of motion

Newton's First Law

• Law of inertia - in the absence of an outside force, the motion of an object remains unchanged.

Newton's Second Law

• force alters motions - produces acceleration.

$$F = ma$$ $$Force = mass * acceleration$$

The mass must be given in kg!

For several forces: $$F_{net} = \sum{F} = ma$$

For a given force, the more mass = the less acceleration.

Force is a vector and has a direction.

• The unit of force is a Newton.
• $$Newton (N) = kg * m/(s^2)$$

1 pound = 4.45 N

Newton's Third Law

Two objects in contact with each other exert equal forces on each other pointing in opposite directions.

• If the earth exerts 150lb force on a human due to gravity, the human exerts a -150lb force on earth as well.

Four Main Forces

Force of Gravity

$$Weight (W) = F_{gravity}$$

Normal Force

When an object is in contact with a surface, the surface exerts a force pointing towards the object at right angles to the surface.

sa. the Ground exerts a force upwards on a human.

You figure out the normal force by difference.

$$Normal force abbreviation is n or F_{n}$$

Tension

• Anything that stretches or is elastic.
• Exerts a force in a direction opposite the free end.

For a spring, hooke's law: $$T = -kx$$

• T is the force of tension from the spring
• k is a spring constant that depends on the spring.
  • How much force it takes to stretch a unit amount.
  • N/m - newton's per meter.
  • k gets bigger as a spring gets stiffer.
• x is how far the spring is stretched.
  • Negative when compressed, positive when stretched.

Negative because the direction of stretch is opposite the direction of the force.

• Other than for a spring, it acts like a normal force, you have to figure it out based on the net difference with other forces.

Friction

Kinetic Friction

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Static Friction

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Kinetic Friction

• Friction when an object is moving.

• Force is parallel to surface and opposite the direction of motion. $$f_{k} = -(mu)_{k} * N$$

• mu_k is unitless, based on surface, a coefficient of kinetic friction.

• N is the normal force experienced by an object.

Static Friction

• For objects at rest on a surface.

• Force is parallel to surface and opposite the direction of motion. $$f_{x} = <= -(mu)_{s} * N$$

• mu_k is unitless, based on surface, a coefficient of static friction.

  • This is different than the coefficient of kinetic friction!
  • Related to the roughness of an object.

• N is the normal force experienced by an object.

• F_s adjusts itself to value to keep object at rest

  • adjustable value that has a maximum

• If object moves, static friction is replaced by kinetic friction.

• If f_s exceeds mu_s*N, then the object begins to slide.

• f_s is the maximum value of static friction, exact value depends on context and other forces.