Chapter 8: Rotational Motion

  1. Angular Quantities

    1. Angular position is equal to the angle θ of a line

    2. For calculations in rotational motion angles are measured in radians

      1. Make sure the calculator is in radians when calculating any angular motion

      2.  Θ = l/r

    3. Angular velocity: ω = θ/t

    4. Angular velocity has units of radians/sec

    5. All points in a rigid object will rotate with the same angular velocity

    6. Angular Acceleration: α = ω/t

    7. The normal values of any angular value can be found by multiplying the value by r

      1. EX: a = αr, v = ωr

    8. I is equal to inertia and its value differs between objects

      1. The equation for inertia of an object should be given

  2. Rolling Motion 

    1. In order for an object to rotate a frictional force needs to be applied

    2. If there is not friction rather than rolling an object would just slide across the surface

    3. When rolling an object has both rotational and translational motion

  3. Torque

    1. The torque or an object can be found with:

      1. τ = Fperpendicular * r or Frsinθ

      2. τ = Iα *similar to F=ma

    2. The torque relies on the magnitude of the force as well as the distance that force is being applied from the axis

    3. If there are multiple torques the angular acceleration is proportional to the net torque

  4. Rotational Kinetic Energy

    1. An object rotating around an axis has rotational kinetic energy

    2. Rotational Kinetic Energy can be defined as:

      1. K = 0.5(I)(ω)2

    3. When calculating energy equations with rotational energy you do not need to include static friction as static friction is the rotational energy since friction causes the rotation

    4. Work that is done by torque can be calculated as:

      1. W = τ Δθ

    5. Power can be defined as:

      1. P = W/t = (τ Δθ)/t = τω

  5. Angular Momentum

    1. Angular Momentum is:

      1. L = Iω

    2. The net torque can be found using angular momentum:

      1.  Στ = τnet = ΔL/Δt

    3. Angular momentum is a conserved quantity like normal momentum

    4. The total angular momentum or a rotating object remains constant as long as the net torque acting on the object is zero