Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

5.1.6Torque and Rotational Dynamics

Rotational Kinematics Equations — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 10 parts Lesson 7 of 18 1 quiz

📚 AP PHYSICS 1 Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
0%read
Lesson summary

5.1.6 Rotational Kinematics Equations — AP PHYSICS 1 notes: Apply the equations of rotational kinematics for constant angular acceleration to find positions, velocities, accelerations and times.LinearRotationalQuantity not requiredv = v0 + atω = ω0 + αtΔθx = x0 + v0t + ½at2θ = θ0…

  • Conditions
  • Quantities
  • Equation sheet
  • Five variables
  • Alternatives
  • Steady friction

Section 1 of 10The equations

LinearRotationalQuantity not required
v = v0 + atω = ω0 + αtΔθ
x = x0 + v0t + ½at2θ = θ0 + ω0t + ½αt2ω
v2 = v02 + 2a(x − x0)ω2 = ω02 + 2α(θ − θ0)t
x = x0 + ½(v0 + v)tθ = θ0 + ½(ω0 + ω)tα
x = x0 + vt − ½at2θ = θ0 + ωt − ½αt2ω0
Conditions
  • α constant, motion about an axis, timer starting at zero.
Quantities
  • ω in rad/s, α in rad/s2, t in s, Δθ in rad.
Equation sheet
  • Equation sheet lists the first three equations; the others are derived.

Section 2 of 10Choosing the equation

Five variables
  • Δθ, ω0, ω, α and t; each equation omits one.
Rule
  • Rule choose the equation that contains the knowns and the unknown and omits the variable you neither know nor need.
Examples
  • Examples no time: ω2 = ω02 + 2αΔθ; no final velocity: Δθ = ω0t + ½αt2.
From rest
  • ω0 = 0 simplifies the equations.

Section 3 of 10Procedure

1
Choose the positive direction and write all signed values.
2
List knowns and unknowns, converting rpm and degrees to rad/s and radians.
3
Select and solve the appropriate equation.
4
Check sign, units and plausibility; convert to revolutions with N = Δθ/2π if asked.

Section 4 of 10Constant α only

Validity
  • Validity the equations fail if the net torque, and so α, varies.
Alternatives
  • Alternatives use graphs or an energy approach.
Steady friction
  • Steady friction a wheel slowing under steady bearing friction has nearly constant α.
Zero α
  • Δθ = ωt.

Section 5 of 10Two-stage problems

1Method
  • Method treat each stage separately, with the final values of one as the initial values of the next.
2Total angle
  • Total angle the sum of the stage angles, which equals the total area under the ω–t graph.
3Table
  • Table list Δθ, ω0, ω, α and t for each stage.

Section 6 of 10Rotating turntable example

  • Turntable at 45 rpm decelerating at 0.8 rad/s2
    • ω0 = 3π/2 rad/s, and Δθ = −ω02/(2α) = 13.9 rad, about 2.2 rotations.

Section 7 of 10Connections to linear quantities

Point speeds
  • Point speeds v = rω and at = rα.
Distance
  • Distance a rim point or a rolling wheel centre travels s = rΔθ.
Analogy
  • ΣF = ma becomes Στ = Iα; ½mv2 becomes ½Iω2; mv becomes Iω.

Section 8 of 10More from the specification

More from the specification
Rotational equations on an inclined slope
  • Rotational equations on an inclined slope rolling cylinders down a gravitational slope on Earth obey constant angular acceleration kinematic relations.
Rigid system
  • System that holds its shape while rotating.
Displacement
  • Change in position.
Vector
  • Quantity with magnitude and direction.

Section 9 of 10Key terms

TermMeaning
Constant angular accelerationα that does not change with time.
Rotational kinematicsEquations linking Δθ, ω0, ω, α and t.
Initial angular velocityThe ω at t = 0.
RevolutionsN = Δθ/2π.

Section 10 of 10Exam technique

1
Using the equations when α is not constant.
2
Using revolutions or rpm without converting.
3
Assuming ω0 = 0 when the object does not start from rest.
4
Inserting a deceleration with the wrong sign.
5
Mixing linear and angular variables in one equation.

Last updated: