Describe, qualitatively, motion in a circular path due to a force perpendicular to the motion as: (a) speed increases if force increases, with mass and radius constant (b) radius decreases if force increases, with mass and speed constant (c) an incre

Published by Patrick Mutisya · 8 days ago

Cambridge IGCSE Physics 0625 – Effects of Forces (Circular Motion)

1.5.1 Effects of Forces on Circular Motion

When an object moves in a circular path, the force that keeps it in that path is always directed

towards the centre of the circle. This is called the centripetal force. The magnitude of the

required centripetal force is given by

\$F_c = \frac{mv^{2}}{r}\$

where

  • \$F_c\$ – centripetal force

  • \$m\$ – mass of the object

  • \$v\$ – speed of the object (tangential speed)

  • \$r\$ – radius of the circular path

Qualitative Relationships

  1. Increasing the force (with \$m\$ and \$r\$ constant) increases the speed.

    From the formula, if \$F_c\$ is increased while \$m\$ and \$r\$ stay the same, \$v\$ must increase

    because \$v^{2}=F_c r/m\$. The object speeds up around the same circle.

  2. Increasing the force (with \$m\$ and \$v\$ constant) decreases the radius.

    Re‑arranging the formula gives \$r = mv^{2}/Fc\$. With \$m\$ and \$v\$ fixed, a larger \$Fc\$ makes \$r\$

    smaller, so the path becomes tighter.

  3. Increasing the mass (with \$v\$ and \$r\$ constant) requires a larger force.

    If \$m\$ is larger while \$v\$ and \$r\$ stay the same, the required centripetal force becomes

    \$F_c = (m v^{2})/r\$, which is directly proportional to \$m\$. A heavier object needs a stronger

    inward force to stay on the same circular path at the same speed.

Summary Table

Quantity ChangedQuantities Kept ConstantEffect on Remaining \cdot ariablePhysical Interpretation
Force \$F_c\$ ↑Mass \$m\$, Radius \$r\$Speed \$v\$ ↑Object moves faster around the same circle.
Force \$F_c\$ ↑Mass \$m\$, Speed \$v\$Radius \$r\$ ↓Path becomes tighter; object turns more sharply.
Mass \$m\$ ↑Speed \$v\$, Radius \$r\$Force \$F_c\$ ↑Heavier object needs a stronger inward pull to stay on the same path.

Suggested diagram: Top‑view of an object moving in a circle with arrows showing the

direction of velocity (tangent) and centripetal force (towards the centre). Include three cases

illustrating (a) higher speed, (b) smaller radius, and (c) larger required force for greater mass.

Key Points to Remember

  • The centripetal force is always perpendicular to the instantaneous direction of motion.

  • Increasing the inward force does not change the direction of motion directly; it changes the

    speed or radius depending on which other quantities are held fixed.

  • Mass, speed, radius, and force are linked by the simple relation \$F_c = mv^{2}/r\$; changing one

    while holding others constant leads to predictable qualitative changes.