MFTai-戴明凤.pptVIP

實驗3：轉動-剛體的轉動運動Lab. 3 : Rotation-Rotational Motion of Rigid Body 實驗目的：測量作用在圓盤上之力矩所產生的角加速度和角速度的大小 證明剛體繞固定軸所做的轉動運動，亦遵守牛頓第二 運動定律。 並探討轉動物體的能量守恆關係。 HyperPhysics Most fundamental concepts are subtracted from the web site: /hbase/hframe.html Rotational Dynamics Circular / Rotational Motion For circular motion at a constant speed v, the centripetal acceleration of the motion can be derived. Basic Rotational Quantities The angular displancement is defined by: For a circular path it follows that the angular velocity is The angular acceleration: i.e., Tangential acceleration: Centripetal acceleration: Radian and Conversions q is a pure number, but commonly is given the artificial unit, radian. One radian: is the angle subtended by an arc length equal to the radius of the arc (s = r). Conversion between degrees and radians Angular Displacement The angular displacement is defined as the angle the object rotates through during some time interval. This is the angle that the reference line of length r sweeps out. Average Angular Speed Instantaneous Angular Speed The average angular speed, ?, of a rotating rigid object is the ratio of the angular displacement to the time interval. Average and Instantaneous Angular Acceleration The instantaneous angular acceleration is defined as the limit of the average angular acceleration as the time goes to 0 Units of angular acceleration are rad/s2 or s-2 since radians have no dimensions. Directions of ? Strictly speaking, the speed and acceleration (w, a) are the magnitudes of the velocity and acceleration vectors. The directions are actually given by the right-hand rule. Rotational Kinematics Under constant angular acceleration, the motion of the rigid object can be described using a set of kinematic equations. These are similar to the kinematic equations for linear motion. The rotational equations have the same mathematical form as the linear equations. Comparison Between Rotational and Linear Equations Relationship B