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Unformatted text preview: Dynamics of Rotation Dynamics of Rotation Consider only the magnitude : τ = Fr sin θ , τ is in Nm (MKS) & Dyne cm (CGS) Where F – applied force r – moment arm θ – angle between F & r θ F Axis Line of Force Moment Arm (r) Torque ( τ ) τ = F x r τ is the Cross Product of the Force vector & Moment Arm Torque ( τ ) : The tendency or ability of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist. Torque ( τ ) : Cross or vector product of the force (F) & moment arm (L) F 1 F F τ = F x L τ = (F)(L) sin θ L 1 L Moment Arm (L) : Distance or displacement between the axis of rotation to the point where the force acts of the object Torque ( τ ) : Could go in either a clockwise (CW) or counterclockwise (CCW) in direction Torque ( τ ) : F 1 F F L 1 L F 1 L 1 F L θ 1 θ τ 1 = (F 1 )(L 1 ) sin θ 1 but θ = sin θ τ = (F )(L ) Torque ( Γ ) : F 1 F F L 1 L F F L θ τ = (F )(L ) sin θ τ = 0 Dynamics of Rotation MOMENT OF INERTIA ( I ) – It is the measure of the object’s resistance to changes in rotational speed about an axis. The greater the value of the mass moment of inertia, the smaller the angular acceleration about an axis (slower rotation) I of a point mass I = mr 2 Axis Moment Arm (r) m I is in kgm 2 (MKS) & gcm 2 (CGS) General form of I I = r ∫ 2 dm Axis Moment Arm (r) Dynamics of Rotation Common Moments of Inertia http://hyperphysics.phyastr.gsu.edu I = cMR 2 c is a fraction Dynamics of Rotation Parallel Axes Theorem I P = I CM + Md 2 Old Axis  The moment of inertia can be calculated if moved to another axis as long as that (new) axis is parallel to the (original) axis that passes through the center of mass and the distance between them is known. Where: I P : Moment of Inertia about another axis that is parallel to the axis that goes through the center of mass. I CM : Moment of Inertia about an axis at the center of mass. M : Mass of the object d  distance between the center of mass and the point of the parallel axis. d New Axis Newton’s Second Law in Rotational Motion τ = FR sin θ for a point mass moving in a circle, F is always perpendicular to the Radius thus τ = FR If F is the net force (F net ) Applying NSLM F net = Ma , where a is the tangential acceleration , a = R α τ net = (Ma)R = M(R α )R τ net = MR 2 α But I = MR 2 (for a point mass) τ net = I α R a = Rα where I is really I = cMR 2 M A bucket of water with a mass of 20kg is suspended by a rope wrapped around a...
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This note was uploaded on 05/19/2011 for the course PHYSICS 10 taught by Professor Darp during the Spring '11 term at Mapúa Institute of Technology.
 Spring '11
 darp
 Force

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