Lesson 4.1 Uniform circular motion

What is uniform circular motion?

The motion of an object travelling at a constant speed in a circle. Examples include: toy plane on a string, carousel in a microwave, spin dryer, ceiling fan, and clock hands.

What is the difference between revolving and rotating?

Revolving: moving in a circle around an external centre point (e.g. ball on string revolves around your hand or Earth revolves around Sun). Rotating: spinning around an internal axis (e.g. Earth rotates on its own axis once per day).

What is inertia and how does it relate to circular motion?

Inertia is the tendency of an object to resist change in its motion. According to Newton's first law an object would continue in a straight line unless acted on by an unbalanced force. In circular motion a force must constantly act to change direction.

What is centripetal force? Include symbol and units.

The force acting on an object in circular motion that constantly pulls or pushes it towards the centre of the circle. Symbol: Fᶜ. Unit: newton (N). From Latin "centrum" (centre) and "petere" (to seek) meaning "centre-seeking force".

What is centripetal acceleration? Include symbol and units.

The acceleration experienced by an object moving in a circular path directed towards the centre of the circle. Symbol: aᶜ. Unit: m s⁻². It exists because velocity direction is constantly changing even though speed is constant.

Why does an object in uniform circular motion have acceleration even though speed is constant?

Velocity is a vector with both magnitude (speed) and direction. In circular motion the direction continuously changes so velocity changes. Since acceleration is the rate of change of velocity there must be acceleration even at constant speed.

What is the relationship between centripetal force and velocity direction?

The centripetal force vector (Fᶜ) is always perpendicular to the velocity vector (v). Force points toward centre while velocity is tangent to the circle at every point.

What provides the centripetal force in these examples: (a) ball on string (b) car on road (c) Moon orbiting Earth?

(a) Tension in the string. (b) Friction between tyres and road. (c) Gravitational attraction between Moon and Earth.

Why does a front-seat passenger feel pressed against the car door when going around a roundabout?

The car door provides centripetal force pushing the passenger toward the centre of the turn. The passenger's inertia means their body wants to continue straight. They feel "pushed out" but actually the door is pushing them inward to follow the circular path.

A ball on a string undergoes uniform circular motion. After 100 revolutions what are the displacement and average velocity?

Both are zero. Displacement is the straight-line distance from start to finish. After complete revolutions the ball returns to its starting position so displacement = 0. Average velocity = displacement/time = 0. (Note: average speed is NOT zero as distance travelled is not zero.