Vertical circular motion

All You Need in One Place

Everything you need for Year 6 maths and science through to Year 13 and beyond.

Learn with Confidence

We’ve mastered the national curriculum to help you secure merit and excellence marks.

Unlimited Help

The best tips, tricks, walkthroughs, and practice questions available.

0/2
?
Examples
Lessons
  1. Uniform vertical circular motion

    A 0.315 kg ball attached to the end of a 0.700 m string is swung in a vertical circle so that it has a constant speed of 4.50 m/s. What is the tension in the string at the top and bottom of the circular path?

    1. Minimum speed to keep an object on a vertical circular path

      A 0.245 kg ball is attached to the end of a 0.950 m string and swung in a vertical circle. Find the minimum speed the ball needs at the top of the path to continue travelling in a circle.

      Topic Notes
      ?
      In this lesson, we will learn:
      • Solving problems involving vertical circular motion

      Notes:

      • An object moving in a circular path is in circular motion. If the speed of the object is constant, it is uniform circular motion.
      • An object in uniform circular motion does experience acceleration, even though its speed is constant. Remember, acceleration is change in velocity, and a velocity is made up of speed and direction. For the object to move in a circle, the direction of its velocity must change constantly. This change in direction is the acceleration, called centripetal acceleration ("centripetal" means "towards the center"). For an object moving in a circular path, the centripetal acceleration vector is always pointed towards the center of the circle.
      • Like any other type of acceleration, centripetal acceleration is caused by a force (called centripetal force). The centripetal force vector also always points towards the center of the circle.
      • In order for an object to be moving in a circular path, the net force acting on the object must be a centripetal force (a force that always is pointed towards the center). When multiple forces act on an object in circular motion, those forces must add up to a centripetal force. It is important to understand that centripetal force is not a separate force that acts on an object. It is a net force which follows a specific rule: it always points towards the center of the circular path.
        • In a horizontal circular motion problem, any forces acting on the object in the vertical direction must balance so that ΣFvertical=0N\Sigma F_{vertical} = 0N (otherwise the object would accelerate vertically). Only horizontal forces will contribute to the net force causing circular motion.
      Period and Frequency

      T=totaltime#ofrevolutionsT = \frac{total time}{\# of revolutions}

      f=#ofrevolutionstotaltimef = \frac{\# of revolutions}{total time}

      T=1fT = \frac{1}{f}

      T:T: period, in seconds (s)

      f:f: frequency, in hertz (Hz)


      Centripetal Acceleration

      ac=v2r=4π2rT2a_{c} = \frac{v^{2}}{r} = \frac{4\pi^{2}r}{T^{2}}

      ac:a_{c}: centripetal acceleration, in meters per second squared (m/s2)(m/s^{2})

      v:v: velocity, in meters per second (m/s)

      r:r: radius, in meters (m)

      T:T: period, in seconds (s)