《大学物理》英文课件10 Rotation教学教材.pptVIP

Rotation Dr. Huaqiu Deng E-mail: hqdeng@scut.edu.cn Translation and Rotation Two kinds of pure motion: - Translation: move along a straight or curved line - Rotation: turn about an axis Translation Rotation Rigid body and fixed axis We care about the rotation of a rigid body about a fixed axis. Rigid body – a body that can rotate with all its parts locked together and without any change in its shape. Fixed axis – a rotation occurs about an axis that does not move. The rotational variables The rotational variables - Angular position, - Angular displacement - Angular velocity - Angular acceleration Angular Position s – length of a circular arc r – radius of the circle Unit of θ: radian or rad (弧度） Angular position - an angle of a reference line relative to a fixed direction (zero angular position) . The reference line is fixed in the body. rev – revolution (公转) Sample problem – angular velocity derived from angular acceleration Problem: a child’s top is spun with angular acceleration α = 5t2- 4t. At t = 0, the top has angular velocity 5rad/s, and a reference line on it is at angular position θ = 2rad. (a) Obtain an expression for the angular velocity. (b) Obtain an expression for the angular position. Solution: (a) (b) Are Angular Quantities Vectors? Yes! Answer: yes Right-hand rule Fixed axis: “+ ”:counterclockwise “–”:clockwise ω α can be vector, θ cannot be a vector Right-hand rule Angular displacement is not a vector Rotation with constant angular acceleration Linear variables Angular variables Relating the linear and angular variables Relating the linear and angular variables Radial component: Tangential component: Sample Problem Problem: a grindstone（磨石） rotates at constant angular acceleration α = 0.35rad/s2. At time t = 0, it has an angular velocity of ω0 = -4.6rad/s, and a reference line on it is horizontal, at the angular position ?0 = 0. (a) At what time after t = 0 is the reference line at the angular positi