AP Physics Section 8-4 Torque

Torque Torque is the rotational analog to linear force. A net torque produces an angular acceleration. Torque is the tendency of a force to rotate an object around a axis, fulcrum, or pivot. The symbol for torque is τ (Greek tau). The units for torque are newton•meters (Nm).

Magnitude of torque is given by: τ = r × F F causes rotation τ = r F F τ = r F sinθ doesn’t cause rotation lever arm torque up, out of paper Direction of the torque vector × up, out of paper down, into paper

The grip right hand rule recall: Clockwise displacement is considered negative. Counterclockwise displacement is considered positive. Net Torque Στ = τcw + τccw When there is no angular acceleration, Στ = 0. This is called rotational equilibrium.

1. Calculate the torques on the wrench. b. 0.20 m 131.4° 0.20 m 120 N 90° c. 120 N τ = r F sinθ 41.4° 180° 0.15 m τ = (0.20) (120N) sin90° τ = (0.20) (120N) sin131.4° τ = 24 Nm τ = 18 Nm τ = 0 Nm

2. Calculate the net torque (magnitude and direction) on the beam due to the forces shown. The axis of rotation is perpendicular to the page. F1 = 11 N, F2 = 23 N, and F3 = 15 N If point 1 is pivot: 1 2 3 Torques about point 1 τ1 = r1 F1 sinθ Since r1 = 0, τ1 = 0 Nm τ2 = r2 F2 sinθ τ2 = (3.0 m)(23 N)sin+90° τ2 = +60 Nm (CCW) τ3 = r3 F3 sinθ τ3 = (4.0 m)(15 N)sin–45° τ3 = –42 Nm (CW) Στ = +18 Nm Up out of page

If point 3 is pivot: Στ = –45 Nm Torques about point 3 τ1 = r1 F1 sinθ 2 3 Torques about point 3 τ1 = r1 F1 sinθ τ1 = (4.0 m)(11 N)sin–30° τ1 = –22 Nm (CW) τ2 = r2 F2 sinθ τ2 = (1.0 m)(23 N)sin–90° τ2 = –23 Nm (CW) τ3 = r3 F3 sinθ Since r3 = 0, τ3 = 0 Nm Στ = –45 Nm Down into page

τA + τB τcw = τcw = τccw = τA = rA FA sinθ τA = τB = rB FB sinθ τB = 24. Calculate the net torque about the axle of the wheel shown in the figure. A B C Στ = τcw + τccw Clockwise: τA + τB (0.12 m)(35 N) sin–90° τA = rA FA sinθ = τA = –4.20 Nm τB = rB FB sinθ (0.24 m)(18 N) sin–90° = τcw = (–4.20)+(–4.32) τB = –4.32 Nm τcw = –8.52 Nm Counterclockwise: τC = rC FC sinθ (0.24 m)(28 N) sin+90° = τC = τccw = +6.72 Nm +6.72 N Στ = (–8.52 Nm) + (+6.72 Nm) = –1.8 Nm