Chapter 9 Rotational ynamics
Chapter 9 Rotational dynamics
9-1 Torque 1,Torque In this chapter we will consider only case in which the rotational axis is fixed in z M direction Fig 9-2 shows an P arbitrary rigid body that is free to rotate about the z axis A force F is applied at point P, which is located a perpendicular distance r from the axis of rotation. Fand r lie in x-y plane, and make an angle 0
9-1 Torque 1. Torque In this chapter we will consider only case in which the rotational axis is fixed in z direction. Fig 9-2 shows an arbitrary rigid body that is free to rotate about the z axis. P z O M F r d M * A force is applied at point P, which is located a perpendicular distance r from the axis of rotation. and lie in x-y plane, and make an angle . → F → F → r
The radial component Fp= Fcos0 has no effect on rotation of the body about z axis Only the tangential component f,= Fsin Produces a rotation about the z axis The angular acceleration also depends on the magnitude of r The rotational quantity torque"T is defined as t=rF sin 0 (9-1) The unit of torque is the Newton-meter (Nm
The radial component has no effect on rotation of the body about z axis. Only the tangential component produces a rotation about the z axis. FR = F cos F⊥ = F sin The angular acceleration also depends on the magnitude of r The rotational quantity “torque” is defined as (9-1) The unit of torque is the Newton-meter ( ) = rF sin N m
When T =0 T=rF sin e If r=o-that is the force is applied at or through the axis of rotation If 8=or 180, that is the force is applied in the radial direction; If F=0
If r=0 -that is the force is applied at or through the axis of rotation; If or , that is the force is applied in the radial direction; If =0. = 0 180 When =0 ? = rF sin → F
2.Torque as a vector t=rEsin e In terms of the cross product the torque Is expressed as 三F F (9-3) Magnitude of rEsin e Direction of t: using righ-hand rule O P
2.Torque as a vector In terms of the cross product, the torque is expressed as (9-3) → → → = r F = rF sin → Magnitude of : Direction of : using righ-hand rule → rF sin P z O M F r d M *