2.9 Circular Motion

• Centripetal force is always directed towards the center
• Circular motion differs from linear motion in terms of angular velocity, period, and frequency.
• Centripetal force is directed towards the center
• Match the force with its direction:

  Centripetal Force ↔️ Towards the center of the circular path

  Friction Force ↔️ Opposite to the direction of motion

  Normal Force ↔️ Perpendicular to the surface

  Tension Force ↔️ Along the string/rope
• Match the term with its definition, formula, and unit:

  Angular Velocity ↔️ Rate of change of angular position ||| $\omega =$$\frac{\Delta \theta}{\Delta t}$ ||| rad/s

  Period ↔️ Time to complete one full revolution ||| $T =$$\frac{1}{f}$ ||| s

  Frequency ↔️ Number of revolutions per second ||| $f =$$\frac{1}{T}$ ||| Hz
• Uniform circular motion occurs when an object moves at a constant angular velocity.


  True
• Non-uniform circular motion results in both centripetal and tangential acceleration.
• A car accelerating through a turn experiences non-uniform circular motion.

  True
• What is the direction of centripetal force in circular motion?

  Towards the center
• Centripetal force is always directed towards the center
• Match the force with its direction:

  Centripetal Force ↔️ Towards the center of the circular path

  Friction Force ↔️ Opposite to the direction of motion

  Normal Force ↔️ Perpendicular to the surface

  Tension Force ↔️ Along the string/rope
• The centripetal force formula is F_{c} = \frac{mv^{2}}{r}
• A 2 kg object moving at 5 m/s along a circular path with a radius of 2 meters requires a centripetal force of 25 N.


  True
• Steps to solve centripetal force problems:

  1️⃣ Identify variables: mass $(m)$, velocity $(v)$, and radius $(r)$

  2️⃣ Calculate centripetal force using $F_{c} =$$\frac{mv^{2}}{r}$

  3️⃣ Interpret the result in Newtons (N)
• The tension in a string of a swinging 0.5 kg ball moving at 4 m/s with a radius of 0.8 meters is 10 N.
• Match the property with its description:

  Tangential Speed ↔️ Speed along the circumference

  Angular Velocity ↔️ Rate of change of angular position

  Units of Tangential Speed ↔️ m/s

  Units of Angular Velocity ↔️ rad/s
• Angular velocity is defined as the rate of change of angular position.
• A merry-go-round that completes one rotation in 10 seconds has an angular velocity of 0.628 rad/s.
• In circular motion, position corresponds to angular position
• Match the term with its definition, formula, and unit:

  Angular Velocity ($\omega$) ↔️ Rate of change of angular position; $\omega =$$\frac{\Delta \theta}{\Delta t}$; rad/s

  Period (T) ↔️ Time to complete one full revolution; $T =$$\frac{1}{f}$; s

  Frequency (f) ↔️ Number of revolutions per second; $f =$$\frac{1}{T}$; Hz
• Non-uniform circular motion involves both centripetal and tangential acceleration.

  True
• Centripetal force is always directed towards the center of the circular motion.
• Match the type of force with its direction:

  Centripetal Force ↔️ Towards the center of the circular path

  Friction Force ↔️ Opposite to the direction of motion

  Normal Force ↔️ Perpendicular to the surface

  Tension Force ↔️ Along the string/rope
• To calculate centripetal force, you must identify mass, velocity, and radius.


  True
• What is tangential speed in circular motion?

  Speed along a circular path
• The centripetal force for a car turning is provided by friction
• Tangential speed is the speed of an object along the circumference of a circular path


  True
• What are the units for angular velocity?

  rad/s
• In gravitational circular motion, the centripetal force is provided by the force of gravity.
• What is circular motion defined as?

  Movement along a circular path
• In uniform circular motion, angular velocity is constant.


  True
• What happens to angular velocity in non-uniform circular motion?

  It changes over time
• In uniform circular motion, the period of revolution is constant
• Give an example of uniform circular motion.

  Car moving at constant speed
• A car accelerating through a turn is an example of non-uniform circular motion.


  True
• What is the formula for angular velocity ($\omega$)?


  $\omega =$$\frac{\Delta \theta}{\Delta t}$
• The period of circular motion is the time to complete one full revolution
• What is the angular velocity of a merry-go-round that completes one rotation in 10 seconds?

  0.628 rad/s
• What is the direction of centripetal force?

  Towards the center
• Centripetal force keeps an object moving in a circular path instead of a straight line.

  True