Circular Motion: Angular Speed and Centripetal Force
An object going round at steady speed is still accelerating, because the direction of its velocity keeps changing. The resultant force points to the centre and has size mv squared over r, which is also m omega squared r.
What a learner can do afterwards
- Converts between period, frequency, linear speed and angular speed in radians per second
- Names the real force acting as the centripetal one in a given setup instead of adding a new force
- Finds the greatest speed for a whirled mass before the string reaches its breaking tension
1 · Read
Rotation uses the radian: arc length over radius, with 2 pi per full turn. Angular speed is angle per second, tied to frequency by omega equals 2 pi f and to period by 2 pi over T. Every point on a disc shares one omega, but rim points move faster since v equals omega r.
Centripetal force is not a new force but a job title. On a whirled ball it is string tension, on a cornering car it is tyre friction, on the Moon it is gravity. Inertia tries to carry things straight while the real force hauls them round. There is no outward force in this picture.
Demand grows as m v squared over r. Spin a 0.5 kg ball on a 1 m string that snaps at 50 N. Setting 0.5 times v squared over 1 equal to 50 gives v equals 10 metres per second. Past that demand the string snaps or the car slides.
Link angle, speed, and time in radians, name the real inward force, and check the demand before it snaps.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.