Physics

I = MR²

I = 1/2 MR²

I = 3/2 MR²

I = 1/12 ML²

I = 1/3 ML²

I = 2/3 MR²

I = 2/5 MR²

I = 7/5 MR²

I = 1/12 ML²

I = 1/12 M(L² + W²)

ω_f = ω₀ + αt

Θ_f = Θ₀ + 1/2 (ω₀ + ω_f)t

Θ_f = Θ₀ + ω₀t + 1/2αt²

ω_f² = ω₀² + 2αΘ

v_t = rω

a_cp = rω<sup>2

Centripetal acceleration is due to a change in direction of motion.</sup>

a_t = rα

Tangential acceleration is due to a change in speed.

ω = v/r

Rolling motion is a combination of translational and rotational motions. An object of radius r, rolling without slipping, translates with linear speed v and rotates with angular speed.

• Θ = s/r
• s = arc length
• r = radius

ω = ΔΘ/Δt

Θ in radians/sec

α = Δω/Δt

Rate of change of angular velocity

T = 2π/ω

T = time required to complete one full rotation if the angular velocity is constant

K_rot = 1/2 Iω²

I = moment of inertia

K = 1/2 mv² + 1/2 Iω<sup>2

can also be written as</sup>

• K = 1/2 mv² + 1/2 I (v/r)²
• = 1/2 mv² ( 1 + I/mr²)