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5.1Torque and Rotational Dynamics

Rotational Kinematics — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 8 parts Lesson 2 of 18 1 quiz

📚 AP PHYSICS 1 Hub / Topical Revision
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Lesson summary

5.1 Rotational Kinematics — AP PHYSICS 1 notes: Describe the rotation of a system over time using angular displacement, angular velocity and angular acceleration.Rigid system — a system that holds its shape although different points move in different directions and with different…

  • Not a point object
  • Centre of mass
  • Rigid body
  • Angular displacement Δθ
  • Average angular velocity
  • What the symbols mean

Part 1 of 6Rotating rigid systems

Rotating rigid systems
Rigid system
  • Rigid system a system that holds its shape although different points move in different directions and with different speeds.
Not a point object
  • Not a point object a rigid system cannot be modelled as a single object;
    • its size and mass distribution matter.
Centre of mass
  • Centre of mass if the rotation about an axis can be described by the centre of mass motion, the system may be treated as one object.
    • (Earth's rotation is negligible for its orbit)
Rigid body
  • Rigid body all points share the same θ, ω and α.

Part 2 of 6Angular variables

1Angular displacement Δθ
Angular displacement Δθ angle through which a point rotates about an axis, in radians; 1 rev = 2π rad; revolutions = Δθ/2π.
2Average angular velocity
  • ωavg = Δθ/Δt in rad/s; ω = 2π/T.
    What the symbols mean: ω = angular frequency (rad s−1) · f = frequency (Hz) · T = period (s)
3Average angular acceleration
  • αavg = Δω/Δt in rad/s2.
4Sign
  • Sign counterclockwise is usually positive.
5Speeding up or slowing
  • Speeding up or slowing same signs of ω and α speed it up; opposite signs slow it down.
6Conversion
  • Conversion rev/min × 2π/60 = rad/s.

Part 3 of 6Constant angular acceleration equations

LinearRotational
v = v0 + atω = ω0 + αt
x = v0t + ½at2θ = ω0t + ½αt2
v2 = v02 + 2aΔxω2 = ω02 + 2αΔθ
Validity
  • Validity constant α only.
Analogy
  • θ, ω, α correspond to x, v, a with the same mathematics.

Part 4 of 6Graphs

θ–t slope
  • θ–t slope gives ω.
ω–t slope
  • ω–t slope gives α.
ω–t area
  • ω–t area gives Δθ.
α–t area
  • α–t area gives Δω.

Part 5 of 6Solving rotational kinematics problems

1
Choose a positive rotation direction (usually counterclockwise).
2
Convert all angles to radians and speeds to rad/s.
3
List the known variables (θ, ω0, ω, α, t) and the unknown.
4
Choose the constant-α equation that omits the variable you do not need.
5
Solve and convert to revolutions if asked.

Part 6 of 6More from the specification

Vector
  • Quantity with magnitude and direction.
Distance
  • Total length of path travelled, a scalar.

Key terms

TermMeaning
Angular displacementAngle turned, in radians.
Angular velocityΔθ/Δt in rad/s.
Angular accelerationΔω/Δt in rad/s2.
RadianArc length divided by radius; 2π rad = 360°.
PeriodTime for one revolution; ω = 2π/T.
Rigid systemSystem that holds its shape while rotating.

Avoid these mistakes

1
Using degrees or rpm directly in the equations.
2
Forgetting that the equations need constant α.
3
Mixing up revolutions and radians.
4
Ignoring the sign convention for direction.

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