A.4 Rigid body mechanics

Objective notes

12 learning objectives

—A.4.1 (HL)—Torque

• Torque about an axis: τ = Fr sin θ.

—A.4.2 (HL)—Rotational equilibrium

• Bodies in rotational equilibrium have a resultant torque of zero.

—A.4.3 (HL)—Unbalanced torque

• An unbalanced torque applied to an extended, rigid body will cause angular acceleration.

—A.4.4 (HL)—Angular motion quantities

• The rotation of a body can be described: angular displacement, angular velocity and angular acceleration.

—A.4.5 (HL)—Angular motion equations

• Use rotational SUVAT equations under uniform angular acceleration.

• Variables include θ/Δθ, angular speed ω and angular acceleration α.

—A.4.6 (HL)—Moment of inertia

• Moment of inertia depends on mass distribution about the rotation axis.

—A.4.7 (HL)—Point-mass moment of inertia

• Point-mass moment of inertia: I = Σmr^2.

—A.4.8 (HL)—Rotational Newton’s second law

• Rotational Newton’s second law: τ = Iα.

—A.4.9 (HL)—Angular momentum

• Angular momentum of a rotating body: L = Iω.

—A.4.10 (HL)—Angular momentum conservation

• Angular momentum remains constant unless the body is acted upon by a resultant torque.

—A.4.11 (HL)—Angular impulse

• Angular impulse changes angular momentum: ΔL = τΔt = Δ(Iω).

—A.4.12 (HL)—Rotational kinetic energy

• Rotational kinetic energy: Ek = 1/2Iω^2 = L^2/2I.