Physics Exam 2

kinetic energy equation

½ mv²

work energy principle

change in kinetic energy

total mechanical energy =

KE + PE

mechanical energy stays constant as long as no

nonconservative forces do work

radial (centripetal) acceleration

a_R = v2/r

where is acceleration directed at in uniform circular motion

center of the circle

frequency

number of revolutions per second

period

time required fro one complete revolution

period equation

1/f

net force equation for UCM

m v²/r

conservative forces

do not change direction of work

nonconservative forces

do change/depend on direction of work

apparent weight

the force an object appears to exert on a scale/surface

gravitational potential energy equation

PE_G=mgy

elastic potential energy

PE= ½ kx²

law of conservation of energy

total energy can be transformed and transferred but total amount remains constant in system

dissipative forces

reduce mech. energy, but not total energy, due to friction

work done by nonconservative forces

W_NC= -F_Frd

Power

rate at which work is done

power equation

P= W/t

power in terms of net force applied

P= Fv

linear momentum equation

p=mv

newton’s second law in terms of momentum

F= m v/t

if no external forces act on a system,

the momentum is a conserved quantity

the more momentum an object has,

the harder is it to stop it

impulse equation

F (t) = change in p

elastic collision

two hard objects collide and no energy is produced in collision; total KE is same before and after

if KE is conserved during a collision then,

it is an elastic collision

if KE is not conserved during a collision then,

it is an inelastic collision

objects in elastic collisions bounce away

at same speed as beginning

objects in inelastic collisions bounce away

at lesser speed than initially

if two objects stick together after a collision,

the collision is completely in inelastic

axis of rotation

all points on a object moving in rotational motion and the center circle lie here

angular position

how far a rotating object has rotated

how to find angular position

specify angle of particular line in object measured along circumference of path

radian

use length distance from axis to calculate

radian equation

$$\theta=\frac{arcleng\operatorname{th}}{r}$$

angular velocity and angular acceleration

are the same at every point in RM

angular displacement

measures how far an object rotates

average angular velocity equation

$$\omega=\frac{\Delta\theta}{\Delta t}$$

instantaneous angular velocity

limit of average angular velocity as t approaches 0

angular velocity units

rad/s

angular acceleration

change in angular velocity over change in time

angular acceleration symbol

$$\alpha$$

do rotating objects with angular velocities have linear velocities

yes, direction is tangent to its circular path

linear velocity equation for RM

$$v=r\omega$$

an object’s linear velocity is _____ for points farther from axis

greater

tangential acceleration of a point on a rotating object

$$a\tan=r\alpha$$

the total linear acceleration of a point in rotation is the vector sum of

tangential acceleration and centripetal acceleration

centripetal acceleration equation

$$aR=\omega^2r$$

$aR$ is ____ the farther from the center

greater

frequency

number of completed revolutions per second

frequency (f) is related to angular velocity by

$$\omega=2\pi f$$

frequency unit

Hertz

period

time required for one complete revolution

period equation

$$\frac{1}{f}$$

rolling objects without slipping requires both

translational and rotational motion

lever arm

distance from axis of rotation of a rotating object

angular acceleration is proportional to

torque

torque symbol

$$\tau$$

the smaller the lever arm,

the least effective in accelerating the object

torque units

m N

which forces only cause rotational acceleration

forces perpendicular to axis of rotation

torque equation

$$\tau=I\alpha$$

rotational inertia symbol

$$I$$

rotational inertia equation

$$mr^2$$

fixed rotational KE equation

$$\frac12I\omega^2$$

moving rotational KE equation

$$\frac12mv^2+\frac12I\omega^2$$

static friction must be present for

an object to roll

does static friction do any work on a rolling object

no, too small to measure

what causes rolling objects to slow down

some gravitational potential energy is converted to rotational KE, leaving less for translational KE

work done by torque equation

$$W=\tau\Delta\theta$$

power from applied torque

$$p=\tau\omega$$

angular momentum equation

$$L=I\omega$$

units for angular momentum

$$\operatorname{kg}\cdot\frac{m^2}{s}$$

Newton’s 2nd law of rotation in terms of angular momentum

$$\tau=\frac{\Delta L}{\Delta t}$$

Law of Conservation of Angular Momentum

the total angular momentum of a rotating object remains constant if the net torque acting on it is zero

center of mass

the point in an object or a system of objects that moves in the same path that a particle would move if subjected to the same force

center of mass of a system equation

$$x_{\operatorname{cm}}=\frac{\left(m_{a}x_{a}+m_{b}x_{b}+m_{c}x_{c}\right)}{M}$$

if one mass in a system is greater than the other, then the CM is

closer to the larger mass

center of gravity is considered to be

the same as center of mass