Centripetal Force, Circular Motion, and Gravitation

Question-and-answer flashcards covering uniform circular motion, centripetal acceleration and force, Newton’s law of gravitation, and key constants and formulas.

What is uniform circular motion?

Motion in a circular path at constant speed, where only the direction of velocity changes.

In uniform circular motion, what happens to the magnitude of velocity and its direction?

The magnitude (speed) stays constant, while the direction continuously changes, producing acceleration toward the center.

What is centripetal acceleration?

The acceleration of an object in circular motion that is directed toward the circle's center.

Toward which direction does centripetal acceleration always point?

Directly toward the center of the circular path.

What formula gives the speed of an object in uniform circular motion?

v = 2πr / T, where r is the radius and T is the period.

What is the period (T) of circular motion?

The time it takes an object to complete one full revolution around the circle.

What is the mathematical expression for centripetal acceleration in terms of speed and radius?

a_c = v² / r.

Which SI units are used for centripetal acceleration?

Meters per second squared (m/s²).

Define centripetal force.

The inward force required to keep an object moving in a circular path at constant speed.

Using Newton’s Second Law, what is the formula for centripetal force?

Fc = m ac = m v² / r.

How does centripetal force depend on mass, speed, and radius?

It is directly proportional to mass and the square of speed, and inversely proportional to the radius of the circular path.

State Newton’s Universal Law of Gravitation in words.

Two masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

What is the equation for the gravitational force between two masses?

F_g = G (m₁ m₂) / r².

What is the value and unit of the gravitational constant (G)?

G = 6.67 × 10⁻¹¹ N·m²/kg².

How does the gravitational constant (G) differ from g, the acceleration due to gravity?

G is a universal constant that is the same everywhere, while g is the local acceleration due to gravity, which varies with location and planetary body.

If a 12.0 kg object moves at 4.3 m/s in a 1.5 m radius circle, what centripetal force acts on it?

F_c = m v² / r = (12.0 kg)(4.3 m/s)² / 1.5 m ≈ 1.5 × 10² N.

What centripetal acceleration does a car experience when traveling 10.0 m/s around a 25.0 m radius track?

a_c = v² / r = (10.0 m/s)² / 25.0 m = 4.0 m/s².