# The Physics of Skateboarding

For students to learn skateboard tricks and relate those movements to the following Physics Concepts: Newton’s 3 laws, gravity, momentum, trajectory projectiles, circular motion, and friction (four types: rolling, sliding, static and air resistance).

1)  Newton’s 1st law (sometimes referred to as the law of inertia): “An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force”.

2)  Newton’s 2nd law:  predicts the behavior of objects for which all existing forces are balanced. Objects at equilibrium (the condition in which all forces balance) will not accelerate. An object will only accelerate if there is a net or unbalanced force acting upon it. The second law states that the acceleration of an object is dependent upon two variables – the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object.

3)  Newton’s 3rd law: For every action, there is an equal and opposite reaction”.

4)  Gravity

5)  Momentum: Momentum vectors are defined as the total motion contained in the object. Product of mass of the object and the velocity is equal to momentum vector. Momentum vector is also known as a vector quantity. Unit for momentum vector is kg m/s (or) kg cm/s. General formula for momentum vector is: p=m x v, where m= mass of the body; v= velocity of the body.

6)  Circular Motion: When an object is experiencing uniform circular motion, it is traveling in a circular path at a constant speed. If r is the radius of the path, and we define the period, T, as the time it takes to make a complete circle, then the speed is given by the circumference over the period. A similar equation relates the magnitude of the acceleration to the speed: $v= (2\pi)/T$ and $a= (2\pi)v/T$.  These two equations can be combined to give: $a=v^2/r$, centripital acceleration. Where there is acceleration, there is a force.   We call the force centripetal force (NOT centrifugal force!), which is described by the formula: $F=mv^2/r$.

7)  Trajectory projectiles:  a projectile is an object upon which the only force acting is gravity. There are the two components of the projectile’s motion – horizontal and vertical motion. The presence of gravity does not affect the horizontal motion of the projectile. The force of gravity acts downward and is unable to alter the horizontal motion. There must be a horizontal force to cause a horizontal acceleration. The vertical force acts perpendicular to the horizontal motion and will not affect it since perpendicular components of motion are independent of each other. Thus, the projectile travels with a constant horizontal velocity and a downward vertical acceleration.

8)  Rolling Friction:When a cylinder rolls on a surface the force resisting motion is termed rolling friction.  Rolling friction is generally considerably less than sliding friction.    If W is the weight of the cylinder converted to force, or the force between the cylinder and the flat surface, and R is radius of the cylinder and F is the force required to overcome the rolling friction then.

9)  Sliding Friction: When the tangential force F overcomes the frictional force between two surfaces then the surfaces begins to slide relative to each other.   In the case of a body resting on a flat surface the body starts to move.    The sliding frictional resistance is normally different to the static frictional resistance.    The coefficient of sliding friction is expressed using the same formula as the static coefficient and is generally lower than the static coefficient of friction.

10) Static Friction: The static friction coefficient ($\mu$) between two solid surfaces is defined as the ratio of the tangential force (F) required to produce sliding divided by the normal force between the surfaces (N).

11) Air Resistance Friction: Air friction is due to the object moving through the air having to move molecules of air aside.

 Physics concept Skateboard Trick Explanation of Trick 1) Newton’s 1st law (1a) Canyon Jump Ollie (1a) Skater will keep moving forward as long as he is not acted upon by an outside force  (e.g. concrete wall) (1b) Chair Nollie (1b) Skater will keep moving forward as long as he is not acted upon by an outside force  (e.g. small chair) (1c) Half pipe drop in (1c) Skater will not move or continue to stay at rest unless acted upon by an outside force  (e.g. Gravity pulling him down)

A physics problem:

A man walking with aid of a cane approaches a skateboard (mass 3.5 kg) lying on the sidewalkk. Pushing with an angle of 60 down from the horizontal with his cane, he applies a force of 115N, which is enough to roll the skateboard out of the way.
a) calculate the horizontal force acting on the skateboard
b) calculate the initial acceleration of the skateboard.