Presentation on theme: "Review Chap. 10 Dynamics of Rotational Motion"— Presentation transcript:
1Review Chap. 10 Dynamics of Rotational Motion PHYS 218 secReviewChap. 10Dynamics of Rotational Motion
2What you have to know Dynamics of rotational motion Torque Equation of motion for a rotational motionRotation about a moving axisWork & powerAngular momentum and its conservation
3Translational motion: governed by forces TorqueTranslational motion: governed by forcesRotational motion: governed by torquesWhen you define a rotational motion, you should specify the axis of rotation. Therefore, physical quantities in rotational motion must include information about the location of the axis of rotation.This makes the definitions of those physical quantities include x or r.For example, even if the same force (same magnitude & same direction) is applied, the rotational motion depends on where the force exerts on, i.e., the distance between the axis of ration and the point where the force exerts on.When you have a rotational motion, determine whether the rotation is clockwise or counterclockwise.
4This force causes counterclockwise rotation. (So, t is positive) TorquedefinitionThis force causes counterclockwise rotation. (So, t is positive)Axis of rotation
5Line of action of the force F TorqueLine of action of the force FLever armOnly the tangential force can give a torque.
6Note the similarity of the two equations. Torque for a rigid bodyNote the similarity of the two equations.Rotational analog of Newton’s 2nd law for a rigid body
7Reproduce the result of Ex 9.8 as explained in the class Same situation as in Ex 9.8Free-body diagramReproduce the result of Ex 9.8as explained in the classDirection of the rotation & sing of the torque
8Ex 10.3Same situation as in Ex 9.9Free-body diagramcylinderblockObtain v !
9Rigid-body rotation about a moving axis Extend the analysis to the case where the axis of rotation movesTranslation + Rotationcm
12Translation + Rotation For translation, concentrate the mass of the object on its CM g same as the motion of a point-like particleFor rotation, consider the rotation about CM g same as the rotational motion when the CM is fixed.The second equation is valid, ifThe axis through the CM must be an axis of symmetryThe axis must not change direction
13Speed of a primitive yo-yo Ex 10.4Speed of a primitive yo-yoinitialfinal
14Race of the rolling bodies Ex 10.5Race of the rolling bodies
15Acceleration of a primitive yo-yo (cf. Ex 10.4) Rolling without slippingTry to reproduce the result of Ex 10.4
16Solid bowling ball (rolling without slipping) Ex 10.7Solid bowling ball (rolling without slipping)Free-body diagramIf b is small, the friction force which is required to have the rolling is small.If b is large, the ball easily slips, then we need a large friction force to make it roll.
17Work & Power in rotational motion To rotate a body, a force should be applied. Then this force do work on it.
19Similarly, we define angular momentum L (linear) momentum pSimilarly, we define angular momentum LThis is defined with r, so it depends on the choice of the origin.This is a vector product. Therefore, the angular momentum is perpendicular to the plane spanned by r and p. If r and p lie on the xy-plane, L is in the z-direction.This is always true.
26Collision problem including rotational motion. Ex 10.14Collision problem including rotational motion.g use angular momentum conservationdafterbeforeUse the numbers given in the textbook to verify the result.Also check the change in kinetic energies.
27Gyroscopes & precession The motion of gyroscope was discussed in the class.Here I do not repeat it.But you should understand that the gyroscope has precession and this is due to the vector nature of angular momentum.