That’s How I Roll

If you have hung around in a science-y place (like all cool kids do these days), you may have seen the following diagram.

That's How I Roll

Kudos if you laughed (or groaned). If not, I shall try to explain the humour behind it (and consequently kill the joke). In essence it shows the system of forces that act as a wheel rolls down an inclined plane.

  • The plane is inclined at an angle θ (theta). This Greek letter is commonly used to represent an angle. Due to alternate angles, the angle that Vcm makes to the horizontal is also θ.
  • The centre of mass is the point in an object where all of its mass can be considered to be. This wheel is two dimensional, and it is assumed to be a perfect circle, so its centre of mass lies at the centre (unsurprisingly).
  • mg is the force that represents the weight of the wheel. It acts downwards from the centre of mass of the wheel, as does the weight of every object on the surface of the Earth. m is the mass of the wheel, and g is the gravitational field strength of the Earth. The weight of an object is given by its mass multiplied by gravitational field strength, which is why it is represented by mg. It is the weight of the wheel that causes it to roll down the plane.
  • Because the wheel has a weight, a normal force (or reaction force or support force) Fn acts on the wheel perpendicular to the plane. This is the plane pushing up on the wheel. If there was no normal force, the wheel would fall through the plane, and we know from reality that things don’t fall through the ground.
  • The plane is also not perfectly smooth, so there is frictional force fs that acts at the point where the wheel and the plane are in contact. The frictional force causes the wheel to roll down the plane, not to slide.
  • Vcm is simply used to show the direction and speed of the wheel (the V stands for velocity). It is important that it refers to the centre of mass, because the centre moves in a straight line. Any point around the centre would rotate as it rolls. The direction of movement of the wheel is parallel to the plane, and is therefore at an angle θ below the horizontal.
  • ω (omega) is the Greek letter used to represent angular velocity. This is the rate at which an object rotates, as opposed to the speed at which an object moves.
  • R is the radius of the wheel.
  • Vcm = Rω is a formula that can determine how fast the wheel moves from its radius and its angular velocity.

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