Unit 7 - Torque and Rotational Motion (12-18%)

Question 1

rotational motion

Answer 1

when an object rotates about a fixed axis (as opposed to linear motion like in all other units)

Question 2

the smaller the radius of rotation, ____.
the linear distance a wheel moves is ____.

Answer 2

the shorter distance the circle travels,
proportional to its radius

Question 3

symbol for angular velocity, rate, and unit:

Answer 3

w (omega), change in theta/change in time, radians per second (rad/s)

Question 4

symbol for angular acceleration, rate, and unit:

Answer 4

a (alpha), change in angular velocity/change in time, radians per second squared (rad/s^2)

Question 5

formula for converting rotational distance to linear distance:

Answer 5

distance = (radius)(angular quantity theta)

Question 6

equation for centripetal acceleration (accel. of object in a circular motion) and relationship when variables change

Answer 6

accel. = (w)^2(radius)
smaller the radius, the smaller the acceleration

Question 7

torque verbal definition and unit
what causes an object to move:

Answer 7

when a force applied to an object causes the object to rotate, unit is m * N
when a component of the force is perpendicular to the radius of rotation

Question 8

torque formula

Answer 8

T = (r perpendicular to axis of rotation)(F)(sinӨ)

either radius is perpendicular to force or vice versa

Question 9

rotational inertia/moment of inertia definition

Answer 9

the tendency of a body to resist a rotation (capital I symbol)

Question 10

why more mass doesn’t mean an object will rotate faster/objects of same mass may not rotate at same rate:

Answer 10

mass distribution is different, better mass distribution, easier to get it to rotate (ex. solid sphere rotates faster than hoop of same mass)

Question 11

rotational inertia/moment of inertia equation and unit

Answer 11

I = m1(r1)^2 + m2(r2)^2 + …..
unit is kg(m)^2

Question 12

Newton’s 2nd Law in Rotational Form

Answer 12

net Torque = (moment of inertia I)(angular acceleration a)

Question 13

in order for a pulley that has mass to undergo angular acceleration

Answer 13

there must be a net torque (tensions in string from both sides CAN’T be equal!)

Question 14

rotational kinetic energy (definition and formula)

Answer 14

the kinetic energy of an object that rotates from one point to another with some velocity
Kr = 1/2(moment of inertia I)(angular velocity w)^2

Question 15

(talking about rotational kinetic energy) the larger the rotational inertia, ___.

Answer 15

the more rotational kinetic energy the object will have at the bottom, and less translational kinetic energy it will have at the bottom

Question 16

angular momentum (both equations) and unit

Answer 16

wangular momentum L = (rotational inertia I)(angular velocity a) = (m)(linear velocity v)(radius r)

unit is kg*m^2/sec
note: is a vector quantity (direction associated w/it)

Question 17

general sign of clockwise/counterclockwise directions

Answer 17

CCW is generally positive, CW is generally negative

Question 18

how to convert w/radians and revolutions

Answer 18

2π radians per 1 revolution

Question 19

change in angular momentum:

Answer 19

ΔL = (torque)(change in time)

Question 20

angular momentum is zero when:

Answer 20

the net torque is zero (T CCW - T CW = 0)

Question 21

situations where angular momentum is conserved:

Answer 21

-in any collision
-when the shape or the mass distribution of an object changes
-when there is no outside net torque

Question 22

linear velocity equation in terms of this unit:

Answer 22

v = (radius)(angular velocity w)

note: used w/angular momentum conservation, start with Lo = Lf, put in each individual momentum, choose eq. based on each object’s given information

Question 23

tangential acceleration and centripetal acceleration equations:

Answer 23

At = (radius)(angular velocity w)
Ac = (linear velocity)^2 / (radius)