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Course: Mechanics (Essentials) - Class 11th>Unit 9

Lesson 4: Why can a car not turn on ice?

Centripetal forces review

Review the key concepts, equations, and skills for centripetal forces, including that centripetal force is the net force in the radial direction.

Key terms

Term (symbol)Meaning
Centripetal force (${F}_{c}$)Net force acting in the direction towards the center of a circular path, causing centripetal acceleration. Direction is perpendicular to the object’s linear velocity. Also sometimes called radial force.

Equations

EquationSymbol breakdownMeaning in words
$\mathrm{\Sigma }{F}_{R}=m{a}_{c}$${a}_{c}$ is centripetal acceleration, $m$ is mass, and $\mathrm{\Sigma }{F}_{R}$ is net force in radial direction (or centripetal force)Net radial force is directly proportional to the product of the object's mass and centripetal acceleration.

Common mistakes and misconceptions

• Centripetal force is not a type of force. Centripetal force is a net force is the sum of the force vectors pointing in the radial direction. It could be the component of a force, the sum of multiple forces, or the difference of two radial vectors.
• People mistakenly think objects moving in a circular path are acted upon by an outwards pointing force. When you turn in a circle, it may feel like something is pulling you outwards from the turn, but that’s your inertia trying to resist a change in motion.

For deeper explanations of centripetal force, see our video introducing centripetal force using flaming test balls.
To check your understanding and work toward mastering these concepts, check out the exercise on centripetal forces.

Want to join the conversation?

• ΣF r is net force in radial direction, then it could be the difference of two radial vectors that are pointing in opposite directions? (such as the difference between force of tension and gravitational force) Also, I noticed how the object attached to a string wouldn't actually rotate unless you exert a force that could spin up the string, so it there a notion to explain this? thank you!
• Yes, you are correct. The net force in the radial direction (ΣFᵣ) can indeed be the difference of two radial vectors pointing in opposite directions, like the difference between the force of tension and gravitational force. When these forces are in balance, the object experiences no radial acceleration.

Regarding the object attached to a string not rotating unless you exert a force to spin up the string, this is related to the concept of centripetal force. When an object is moving in a circular path, there must be a force acting towards the center of the circle (centripetal force) to keep it in that circular motion. Without this inward force, the object would move in a straight line due to its inertia. So, in the case of an object attached to a string, if you don't apply enough force to overcome its inertia and provide the necessary centripetal force, it won't rotate and will simply move in a straight line.
• In the roller coaster example, because more forces are added onto the centrifugal force, that means that the centrifugal force gets larger, correct?
• Yes. Remember that the centripetal force is not a type of force in itself (like forces of gravity, tension, or the normal force), but instead just a name we give to any force causing the object to undergo circular motion.
• If physics over complicates things one more time, I'm going back in time and fighting Issac Newton >:(
• yoo this 1v1 boutta be fire
idk tho Xx_1saccNewt0n_xX is pretty op
got number theory and physics lv 100