Torque A torque (due to a force) causes angular acceleration. Torque = (force) x (moment arm) Moment arm is the perpendicular distance between the axis of rotation and the point where the force is applied. Torque = (perpendicular force) x (distance)

Example -- wheel A belt around a wheel in an exercise bike exerts a frictional force of 100 N in the direction shown. What is the torque due to friction on the wheel if the radius of the wheel is 40 cm? F

Poll F F One force acts at a distance R and another force acts at the distance 1/2 R. What is the net torque on the wheel? 1.+FR 2.-FR 3.+1/2 FR 4.-1/2 FR 5.+2FR 6.-2FR

Poll F hand Friction on bolt If you just barely get a wrench to turn, which is larger, the force on the wrench by your hand or the force of friction on the bolt (that you are turning)? 1.Force by hand 2.Force by friction 3.Neither, because they are equal

Newton’s second law for rotation A net torque causes a system to have an angular acceleration. The proportionality constant is the moment of inertia. The moment of inertia I depends on the system’s mass and how it is distributed.

Moment of inertia R Point particle Solid wheel rotating about its center. Sphere rotating about its center. Thin hollow wheel rotating about its center

Example--Moment of Inertia A 50-kg child is on a rotating merry-go-round of mass 300-kg and radius 2 m. If the child is at the edge of the merry-go-round, what is the total moment of inertia of the system?

Example--Newton’s second law for rotation A 50-cm bicycle wheel is rotating at 5 rev/s. If you use your hand to exert a frictional force on the edge wheel, what force is needed to slow the wheel to a stop in 4.0 s?

Poll Which wheel is easier to accelerate, a solid wheel of mass M and radius R or a hollow wheel of mass M and radius R? 1.Sold wheel 2.Hollow wheel 3.Neither, because they have the same mass and radius.

Angular Momentum If the net torque on a system is zero, then Angular momentum is

Example--Angular Momentum A 50-kg child is on a rotating merry-go-round of mass 300-kg and radius 2 m that rotates at a speed of 0.5 rev/s. If the child is initially at the edge of the merry-go- round and then walks exactly to the center of the merry- go-round, what is the new angular speed of the merry- go-round?

Poll An ice skater is spinning with her arms and legs extended outward. When she pulls her arms and legs into her body, her angular momentum 1.Increases 2.Decreases 3.Remains constant

Poll An ice skater is spinning with her arms and legs extended outward. When she pulls her arms and legs into her body, her moment of inertia 1.Increases 2.Decreases 3.Remains constant

Poll An ice skater is spinning with her arms and legs extended outward. When she pulls her arms and legs into her body, her angular speed 1.Increases 2.Decreases 3.Remains constant