3.1 Motion in a Circle

• What is circular motion defined as?

  Movement along a circular path
• The radius in circular motion is the distance from the center of the circle to the object's path
• In what units is angular displacement measured?

  Radians
• Angular velocity is measured in radians per second
• The formula relating linear velocity, radius, and angular velocity is v = r\omega
• What is tangential velocity in circular motion?

  Velocity along the circular path
• The unit of radius is meters
• What is the rate of change of angular displacement called?

  Angular velocity
• Angular displacement is the angle through which an object moves along its circular path
• What is the formula for angular velocity in terms of angular displacement and time?

  $\omega =$$\frac{\Delta \theta}{\Delta t}$
• Arrange the properties of circular motion in the correct order based on their relationships:

  1️⃣ Angular Displacement ($\theta$)

  2️⃣ Angular Velocity ($\omega$)

  3️⃣ Linear Velocity ($v$)
• What is linear velocity in circular motion?

  Speed along the circumference
• The linear velocity and angular velocity are related by the formula v = r\omega</latex>
• In circular motion, what is the definition of angular velocity?

  Rate of rotation
• In the formula $v =$$r\omega$, v</latex> represents the tangential velocity of the object.
• Match the property with its symbol:

  Angular Displacement ↔️ \theta

  Angular Velocity ↔️ \omega

  Linear Velocity ↔️ v

  Radius ↔️ r
• What is the unit of angular velocity?

  radians per second
• In the relationship $v =$$r\omega$, $v$ and $\omega$ are proportional when the radius $r$ is constant
• What is linear velocity in circular motion?

  Speed along the circumference
• Angular velocity is measured in radians per second
• The relationship between linear velocity and angular velocity is $v =$$r\omega$
• Match the velocity with its definition:

  Linear velocity ↔️ Speed along the circumference

  Angular velocity ↔️ Rate of rotation
• What are the units of linear velocity?

  m/s
• What formula relates linear velocity and angular velocity?

  v = r\omega</latex>
• In the formula $v =$$r\omega$, $r$ represents the radius of the circular path
• Linear velocity and angular velocity are proportional when the radius is constant.
• What is centripetal acceleration?

  Acceleration in circular motion
• The formula for centripetal acceleration is $a =$$\frac{v^{2}}{r}$, where $v$ is the linear velocity
• What is the formula for centripetal force according to Newton's second law?

  $F =$$ma$
• Centripetal force is measured in units of Newtons
• What is circular motion?

  Movement along a circular path
• The radius in circular motion is the distance from the center of the circle to the object's path
• Angular velocity is the rate at which angular displacement changes with time.
• What is the unit of angular displacement?

  Radians
• The relationship between angular velocity and angular displacement is $\omega =$$\frac{\Delta \theta}{\Delta t}$, where $\Delta \theta$ is the change in angular displacement
• Linear velocity and angular velocity are directly proportional when the radius is constant.
• What direction does centripetal acceleration always point?

  Towards the center
• The formula for centripetal acceleration is $a =$$\frac{v^{2}}{r}$, wherev</latex> is the linear velocity
• Match the quantity with its unit:

  Centripetal Force ↔️ Newtons

  Mass ↔️ Kilograms

  Centripetal Acceleration ↔️ m/s²
• Steps to solve problems involving circular motion:

  1️⃣ Identify the key properties

  2️⃣ Apply the relevant formulas

  3️⃣ Substitute the given values

  4️⃣ Solve for the unknowns