Circular Motion & Centripetal Force
Animate uniform circular motion with real-time velocity, acceleration, and force vectors. Adjust speed, radius, and mass to see how centripetal acceleration a_c = v²/r changes.
WHAT IS CIRCULAR MOTION & CENTRIPETAL FORCE?
When an object moves in a circle at a constant speed, its direction is constantly changing, meaning it is accelerating. This **centripetal acceleration** is always directed toward the center of the circle. According to Newton's Second Law, this acceleration must be caused by a net force—the **centripetal force**. It is crucial to remember that centripetal force is not a new kind of force; it is provided by physical forces like tension, friction, gravity, or normal force.
HOW TO USE THIS VISUALIZATION
1. **Modify the Radius**: Observe how a smaller radius requires a greater force to maintain the same speed. 2. **Adjust Linear Velocity**: Notice that centripetal acceleration increases with the square of the velocity (). 3. **Toggle Force Components**: See the vector arrows representing the velocity (tangential) and force (inward).
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 2: Force and Translational Dynamics (Topic 2.3)
Learning Objective: 2.3.1
COMMON MISCONCEPTIONS
- Believing "centrifugal force" is a real outward force acting on the object.
- Thinking the net force on an object in uniform circular motion is zero because the speed is constant.
- Assuming velocity is constant (velocity is a vector; its direction changes).
KEY TAKEAWAYS
- Centripetal acceleration always points toward the center of the circle.
- Centripetal force is not a new force, but a role played by existing forces (gravity, tension, friction).
- Velocity is tangent to the circle; its direction changes, hence acceleration exists even at constant speed.
- If the net force vanishes, the object moves in a straight line tangent to the circle.
- Centripetal acceleration always points toward the center of the circle.
- Centripetal force is not a new force, but a role played by existing forces (gravity, tension, friction).
- Velocity is tangent to the circle; its direction changes, hence acceleration exists even at constant speed.
- If the net force vanishes, the object moves in a straight line tangent to the circle.
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): An object moves in a circle of radius at speed . If the radius is doubled while keeping the speed constant, how does the centripetal acceleration change?
Show Answer & Explanation
Answer: It is halved.
Explanation: Since , doubling to results in .
DEEP DIVE: RELATED CONCEPTS
Projectile motion is the motion of an object thrown or projected into the air, subject only to the a...
WHAT IS TORQUE & ROTATIONAL EQUILIBRIUM?Torque is the rotational equivalent of force. It measures how effectively a force can cause an objec...
WHAT IS PROJECTILE MOTION?Projectile motion is the motion of an object thrown or projected into the air, subject only to the a...
WHAT IS TORQUE & ROTATIONAL EQUILIBRIUM?Torque is the rotational equivalent of force. It measures how effectively a force can cause an objec...
