Rolling Motion & Moment of Inertia Race – AP Physics 1

Learning Objectives

Define moment of inertia (I) for various rigid bodies.

Calculate translational vs rotational kinetic energy.

Apply conservation of mechanical energy to rolling objects.

Predict which object reaches the bottom of an incline first based on shape, not mass.

Energy Equations

Object Color Code

Solid Sphere (I = ²/₅ MR²)

Solid Cylinder (I = ¹/₂ MR²)

Hoop (I = MR²)

Sliding Box (I = 0)

Key Insight

A larger geometric coefficient $\beta = \frac{I}{MR^2}$ means more potential energy is converted into rotational kinetic energy, leaving less for translational velocity. Mass and Radius cancel out entirely!

Torque Moment of Inertia Energy AP Physics 1 Unit 5

t0.00 s

Winner--

Incline Angle $\theta$ 20°

Ramp Distance (m) 15 m

Energy Distribution

$U_g$

$K_{trans}$

$K_{rot}$

📝 Quick Quiz▼

1. Which object reaches the bottom of the incline first?

Solid Sphere Hoop Solid Cylinder Sliding Box (Frictionless)

2. As the hoop rolls down down, what fraction of its total kinetic energy is rotational? ($I = MR^2$)

28.5% (2/7) 33.3% (1/3) 50% (1/2) 100%