5.2 Connecting Linear and Rotational Motion

    Cards (75)

    • Match the linear motion concept with its definition:
      Displacement ↔️ The change in position of an object
      Velocity ↔️ The rate of change of position
      Acceleration ↔️ The rate of change of velocity
      Momentum ↔️ The product of mass and velocity
    • Newton's second law for rotation is Iα=I\alpha =τ \sum \tau.

      True
    • Arrange the following linear motion concepts from simplest to most complex:
      1️⃣ Displacement
      2️⃣ Velocity
      3️⃣ Acceleration
      4️⃣ Momentum
    • What is the formula for linear distance in terms of angular displacement and radius?
      s = r\theta</latex>
    • What is the rotational counterpart of displacement in linear motion?
      Angle
    • What does angular momentum measure?
      Tendency to rotate
    • Linear velocity is equal to the product of radius and angular velocity.
      True
    • What equation relates linear velocity and angular velocity?
      v=v =rω r\omega
    • Displacement measures the change in an object's position.

      True
    • Match the linear motion concept with its definition:
      Displacement ↔️ Change in position
      Velocity ↔️ Rate of change of position
      Acceleration ↔️ Rate of change of velocity
      Momentum ↔️ Product of mass and velocity
    • The rate of change of angular velocity over time is called angular acceleration
    • What is the variable used to denote the radius of rotation in linear-angular relationships?
      r
    • How far does a rider travel on a carousel with a radius of 5 meters after one full revolution?
      31.4 meters
    • Steps to convert between linear and angular velocity using the formula v=v =rω r\omega
      1️⃣ Identify the given values for rr and ω\omega
      2️⃣ Multiply the radius by the angular velocity
      3️⃣ The result is the linear velocity vv
    • The formula relating linear acceleration and angular acceleration is a=a =rα r\alpha, where rr is the radius and α\alpha is the angular acceleration
    • What does the moment of inertia measure?
      Resistance to rotational acceleration
    • Match the rotational concept with its example:
      Angle ↔️ A wheel making one complete revolution
      Angular Velocity ↔️ A spinning top completing revolutions per second
      Angular Acceleration ↔️ A fan increasing its speed
      Angular Momentum ↔️ A spinning disk with constant velocity
    • What is the formula for linear velocity (v) in terms of radius (r) and angular velocity (ω)?
      v=v =rω r\omega
    • Match the linear quantity with its corresponding angular quantity:
      Linear Distance (s) ↔️ Angle (θ)
      Linear Velocity (v) ↔️ Angular Velocity (ω)
      Linear Acceleration (a) ↔️ Angular Acceleration (α)
    • If a carousel with a radius of 5 meters takes 2 seconds to reach full speed, the linear acceleration is approximately 1.57 m/s².
      True
    • The formula for angular velocity is ω = v / r.
      True
    • Linear acceleration is defined as the rate of change of linear velocity.
    • The moment of inertia of a uniform rod rotating about its center is 112ML2\frac{1}{12}ML^{2}.

      True
    • What does Newton's second law for rotation state?
      Iα=I\alpha =τ \sum \tau
    • Torque is defined as τ=\tau =Frsinθ Fr\sin\theta
      True
    • What is the angular momentum of a disk with a moment of inertia of 0.5 kg·m² rotating at an angular velocity of 10 rad/s?
      5kgm2/s5 \, \text{kg} \cdot \text{m}^{2} / \text{s}
    • What is the angular momentum of a wheel with a moment of inertia of 0.5 kg·m² and an angular velocity of 10 rad/s?
      5kgm2/s5 \, \text{kg} \cdot \text{m}^{2} / \text{s}
    • Match the rotational concept with its analogous linear concept:
      Angle (θ) ↔️ Displacement (x)
      Angular Velocity (ω) ↔️ Velocity (v)
      Angular Acceleration (α) ↔️ Acceleration (a)
      Angular Momentum (L) ↔️ Momentum (p)
    • What is the formula for linear velocity in terms of displacement and time?
      v=v =ΔxΔt \frac{\Delta x}{\Delta t}
    • The rate of change of angle over time is called angular velocity.
    • Linear and angular quantities are related through the radius of rotation.
    • Linear acceleration is the product of radius and angular acceleration.
    • The units of linear velocity are meters per second.
    • What is the formula for velocity in terms of displacement and time?
      v=v =Δx/Δt \Delta x / \Delta t
    • The measure of rotation around an axis is called the angle
    • Angular momentum is a measure of an object's tendency to rotate.
      True
    • The formula relating linear distance and angle is s=s =rθ r\theta, where ss is the linear distance, rr is the radius, and θ\theta is the angle
    • If a carousel with a radius of 5 meters completes one revolution in 10 seconds, its linear velocity is approximately 3.14 m/s.
    • Match the formula with the quantity and units:
      v=v =rω r\omega ↔️ Linear Velocity, m/s
      ω=\omega =v/r v / r ↔️ Angular Velocity, rad/s
    • A carousel with a radius of 5 meters and an angular acceleration of 0.5 rad/s² has a linear acceleration of 2.5 m/s² at its edge.
      True