So far, we have defined three rotational quantities—
, and
. These quantities are analogous to the translational quantities
, and
.
[link] displays rotational quantities, the analogous translational quantities, and the relationships between them.
Rotational and translational quantities
Rotational
Translational
Relationship
Making connections: take-home experiment
Sit down with your feet on the ground on a chair that rotates. Lift one of your legs such that it is unbent (straightened out). Using the other leg, begin to rotate yourself by pushing on the ground. Stop using your leg to push the ground but allow the chair to rotate. From the origin where you began, sketch the angle, angular velocity, and angular acceleration of your leg as a function of time in the form of three separate graphs. Estimate the magnitudes of these quantities.
Angular acceleration is a vector, having both magnitude and direction. How do we denote its magnitude and direction? Illustrate with an example.
The magnitude of angular acceleration is
and its most common units are
. The direction of angular acceleration along a fixed axis is denoted by a + or a – sign, just as the direction of linear acceleration in one dimension is denoted by a + or a – sign. For example, consider a gymnast doing a forward flip. Her angular momentum would be parallel to the mat and to her left. The magnitude of her angular acceleration would be proportional to her angular velocity (spin rate) and her moment of inertia about her spin axis.
Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle, or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bug's x,y position, velocity, and acceleration using vectors or graphs.
Uniform circular motion is the motion with a constant angular velocity
.
In non-uniform circular motion, the velocity changes with time and the rate of change of angular velocity (i.e. angular acceleration) is
.
Linear or tangential acceleration refers to changes in the magnitude of velocity but not its direction, given as
.
For circular motion, note that
, so that
The radius r is constant for circular motion, and so
. Thus,
By definition,
. Thus,
or
Conceptual questions
Analogies exist between rotational and translational physical quantities. Identify the rotational term analogous to each of the following: acceleration, force, mass, work, translational kinetic energy, linear momentum, impulse.
Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) The plate starts to spin? (b) The plate rotates at constant angular velocity? (c) The plate slows to a halt?
An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is its angular acceleration in
? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the radial acceleration in
and multiples of
of this point at full rpm?
You have a grindstone (a disk) that is 90.0 kg, has a 0.340-m radius, and is turning at 90.0 rpm, and you press a steel axe against it with a radial force of 20.0 N. (a) Assuming the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstone. (b) How many turns will the stone make before coming to rest?
You are told that a basketball player spins the ball with an angular acceleration of
. (a) What is the ball's final angular velocity if the ball starts from rest and the acceleration lasts 2.00 s? (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
