5 Written questions
5 Matching questions
- Center of mass (CM)
- Tangential speed~
- Formula for Angular Momentum
- Re call the equilibrium rule in Chapter 2--that the sum of the forces acting on a body or any system must equal zero for mechanical equilibrium. That is, ∑F = 0. We now see an additional condition. The *net torque* on a body or on a system must also be zero for mechanical equilibrium...
- a L = Iω
where L (angular momentum) translates to linear momentum (p), and I (moment of inertia) translates to mass (m), and ω (angular velocity) translates to velocity (v). This is the translation from rotational (circular world) terms to linear terms (linear world).
- b The average position of the mass of an object. The CM moves as if all the external forces acted at this point.
- c ...(∑T = 0, where T stands for torque). Anything in mechanical equilibrium doesn't accelerate--neither linearly nor rotationally.
- d Spinning motion that occurs when an object rotates about an axis located within the object (usually an axis through its center of mass).
- e ~radial distance × rotational speed.
In symbol form, v ~ rω
5 Multiple choice questions
- I = mr^2
where m = mass, r = distance, I = rotational inertia
- I = 2/5 mr²
- The product of a body's rotational inertia and rotational velocity about a particular axis. For an object that is small compared with the radial distance, it can be expressed as the product of mass, speed, and the radial distance of rotation.
- When no external torque acts on an object or a system of objects, no change of angular momentum can occur. Hence, the angular momentum before an event involving only internal torques or no torques is equal to the angular momentum after the event.
- the straight line around which rotation occurs
5 True/False questions
kinetic energy → Energy of motion, equal to half the mass multiplied by the speed squared. KE=1/2mv^2
work → the amount of time it takes to complete one cycle (1 revolution)
Rotational Velocity (angular velocity) → the speed with which an object moves through an angle for every unit of time; units: RPM (revolutions per minute), rad/s, θ/s
For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as the magnitude of its linear momentum, *mv*, multiplied by the radial distance, *r*. In shorthand notation: → ⁴When the mass of an object is concentrated at the radius r from the axis of rotation (as for a simple pendulum bob or a thing ring), rotational inertia I is equal to the mass m multiplied by the square of the radial distance. For this special case, I = mr².
Linear momentum = mass × velocity → The average position of the mass of an object. The CM moves as if all the external forces acted at this point.