Reading Time: < 1 minuteAngular Velocity (
Centripetal Force (
Centripetal Acceleration (
Circular Motion: Exploring Centripetal Force and Acceleration
What Is Circular Motion?
Circular motion occurs when an object moves in a circular path due to a centripetal force acting toward the centre.
Key Equations in Circular Motion
Angular Velocity (
)
)The rate of change of angular displacement:
![\[ \omega = \frac{\theta}{t} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-2e8c49d139c9d24113e7b731fd37703c_l3.png "Rendered by QuickLaTeX.com")
Where:
- : Angular velocity (rad/s)
: Angular displacement (radians)
: Time (s)
: Angular displacement (radians)
: Time (s)Centripetal Force (
)
)The force keeping an object in circular motion:
![\[ F_c = \frac{mv^2}{r} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-5c804d7f240c8a7f84a87c222070ef36_l3.png "Rendered by QuickLaTeX.com")
Where:
- : Centripetal force (N)
: Mass (kg)
: Tangential velocity (m/s)
: Radius of the circle (m)
: Mass (kg)
: Tangential velocity (m/s)
: Radius of the circle (m)Centripetal Acceleration (
)
)The acceleration toward the center of the circle:
![\[ a_c = \frac{v^2}{r} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-ff17dd9f42185e99b01e3d0ccdbbf876_l3.png "Rendered by QuickLaTeX.com")
Real-Life Applications of Circular Motion
Transportation
- Banking roads help cars maintain circular motion safely
Space Science
- Satellites use gravitational centripetal force to stay in orbit
Engineering
- Centrifuges rely on circular motion for separating substances
Example Problem
A car of mass 
travels at 
around a curve with a radius of 
. Find the centripetal force.
- Formula:
![\[ F_c = \frac{mv^2}{r} \]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3NyIgaGVpZ2h0PSIzOSIgdmlld0JveD0iMCAwIDc3IDM5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBzdHlsZT0iZmlsbDojY2ZkNGRiO2ZpbGwtb3BhY2l0eTogMC4xOyIvPjwvc3ZnPg== "Rendered by QuickLaTeX.com")
- Substitute Values:
![\[ F_c = \frac{1,000 \times 20^2}{50} = 8,000 \, \text{N} \]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyMTkiIGhlaWdodD0iMzkiIHZpZXdCb3g9IjAgMCAyMTkgMzkiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+ "Rendered by QuickLaTeX.com")
![\[ F_c = \frac{1,000 \times 20^2}{50} = 8,000 \, \text{N} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-a821fd851b3b7991df951f56a22ac127_l3.png "Rendered by QuickLaTeX.com")
Common Mistakes in Circular Motion Problems
- Forgetting to square the velocity in centripetal force calculations
- Mixing up angular and tangential velocity
- Misinterpreting the direction of centripetal force (always toward the center)
Practice Questions
- A
mass travels at 
on a circular path of radius 
. Find the centripetal acceleration. - Explain why satellites stay in orbit due to circular motion.
- Describe one application of centripetal force in transportation.
mass travels at 
on a circular path of radius 
. Find the centripetal acceleration.Skinat Tuition | UK most preferred tutors for A-Level success.