A mountain bike rolls through a puddle, and its wheels spin up muddy. The mud does not stay on for long: fleck after fleck lets go of the spinning tire.
Each fleck leaves in a definite direction. Which direction?
Velocity is speed with a direction. An object in uniform circular motion has a speed that never changes, but it also has a direction at every instant.
At any instant, the object moves in the direction its path points right there.
For a circular path, that direction lies on one special straight line: the line that just touches the circle at the object's position, aimed along the path.
This line is called the tangent.
A horse on a steadily turning carousel is in uniform circular motion. At any instant, along which line does its velocity point?
A fleck of mud that lets go keeps the velocity it had, so it leaves along the tangent line at its release point.
Which line is the tangent to a circle at an object's position?
The tangent touches the circle at exactly one point, and it sits perpendicular to the radius drawn to that point. That is how you find it: draw the radius to the point, then take the line perpendicular to it.
A skater rounds a circular rink edge. At her position, how does the tangent sit relative to the radius drawn to her?
One instant later the object is at a new point, with a new tangent. The velocity direction changes from point to point, even though the speed does not.
A fleck of mud sits at the very top of the spinning tire at the instant it lets go. The tire's center is directly below the fleck. Along which line does the fleck leave?
Draw the radius to the fleck: it runs vertically, from the center up to the top of the tire.
The tangent at that point is perpendicular to this radius: a horizontal line.
The fleck leaves along that horizontal tangent line, the way it was traveling.
The fleck leaves along the horizontal tangent at the top of the tire.
A reflective sticker rides a spinning wheel. At one instant the sticker is level with the axle, at the wheel's 3 o'clock position. Along which line does its velocity point at that instant?
Draw the radius to the sticker: it runs horizontally, from the axle out to the 3 o'clock position.
The tangent there is perpendicular to this radius: a vertical line.
The sticker's velocity points along that vertical tangent, the way the sticker is moving.
Its velocity points along the vertical tangent at the 3 o'clock position.
A bead rides a spinning wheel of radius 0.40 m whose center is marked O. At one instant the bead is at the wheel's 12 o'clock position, directly above O. Along which line does the bead's velocity point at that instant?
Sparks fly off the rim of a spinning grinding wheel. In which direction does each spark leave the rim?
What is the name of the line that just touches a circle at an object's position, aimed along the path?