<< Chapter < Page Chapter >> Page >

ω 2 = ω 1 + α t

We shall study detailed aspect of circular motion under constant angular acceleration in a separate module.

Exercises

A flywheel of a car is rotating at 300 revolutions per minute. Find its angular speed in radian per second.

a 10 b 10 π c 10 π c 20 π

Flywheel covers angular displacement of "2π" in one revolution. Therefore, the angular speed in "radian/second" is :

ω = 2 π X 300 60 = 10 π rad / s

Hence, option (b) is correct.

Got questions? Get instant answers now!

A particle is rotating along a circle of radius 0.1 m at an angular speed of π rad/s. The time period of the rotation is :

a 1 s b 2 s c 3 s d 4 s

The time period of rotation is :

T = 2 π r v = 2 π ω T = 2 π ω = 2 π π = 2 s

Note : The input of radius is superfluous here.

Hence, option (b) is correct.

Got questions? Get instant answers now!

A particle is rotating at constant speed along a circle of radius 0.1 m, having a time period of 1 second. Then, angular speed in "revolution/s" is :

a 1 b 2 c 3 d 4

The time period of rotation is :

T = 2 π r v = 2 π ω

Rearranging, the angular speed is :

ω = 2 π T = 2 π 1 = 2 π

Converting to in the unit of revolution per second, the angular speed is :

ω = 2 π rad /s = 2 π 2 π = 1 revolution/s

Hence, option (a) is correct.

Got questions? Get instant answers now!

A particle is moving with a constant angular speed "ω" along a circle of radius "r" about a perpendicular axis passing through the center of the circle. If " n " be the unit vector in the positive direction of axis of rotation, then linear velocity is given by :

a r X ω b r ω n c ω X r d ω X r

The linear velocity is given by the following vector cross product,

v = ω X r

We know that a change in the order of operands in cross product reverses the resulting vector. Hence,

v = r X ω

Further, it is given in the question that positive axial direction has the unit vector "n". But, the plane of motion is perpendicular to axis of rotation. Hence, velocity is not aligned in the direction of unit vector n .

Hence, options (a) and (b) are correct.

Got questions? Get instant answers now!

The figure shows the plot of angular displacement and time of a rotating disc. Corresponding to the segments marked on the plot, the direction of rotation is as :

Angular displacement

Angular displacement

(a) disk rotates in clockwise direction in the segments OA and AB.

(b) disk rotates in clockwise direction in the segment OA, but in anti-clockwise direction in the segment AB.

(c) disk rotates in anti-clockwise direction in the segment BC.

(d) disk rotates in anti-clockwise direction in the segment CD.

The direction of rotation is determined by the sign of angular velocity. In turn, the sign of angular velocity is determined by the sign of the slope on angular displacement - time plot. The sign of slope is negative for line OA, positive for line AC and zero for line CD.

The positive angular velocity indicates anti-clockwise rotation and negative angular velocity indicates clockwise rotation. The disk is stationary when angular velocity is zero.

Hence, options (b) and (c) are correct.

Got questions? Get instant answers now!

A particle moves along a circle in xy-plane with center of the circle as origin. It moves from position Q(1, √3) to R(-1, √3) as shown in the figure. The angular displacement is :

Angular displacement

Angular displacement

a 30 ° b 45 ° c 60 ° d 75 °

In order to find angular displacement, we need to find initial and final angular positions. From the geometry,

Angular displacement

Angular displacement

tan θ 1 = 3 1 = 3 = tan 60 0 θ 1 = 60 0

Similarly,

tan θ 2 = - 3 1 = - 3 = tan 120 0 θ 2 = 120 0

Thus, angular displacement is :

Δ θ = θ 2 θ 1 = 120 0 60 0 = 60 0

Hence, option (c) is correct.

Got questions? Get instant answers now!

Select the correct statement(s) :

(a) The direction of angular velocity is tangential to the circular path.

(b) The direction of angular velocity and centripetal acceleration are radial towards the center of the circle.

(c) The linear velocity, angular velocity and centripetal accelerations are mutually perpendicular to each other.

(d) The direction of angular velocity is axial.

The direction of linear velocity is normal to radial direction. The direction of centripetal acceleration is radial. The direction of angular velocity is axial. See the figure.

Angular motion

Angular motion

Clearly, the three directions are mutually perpendicular to each other.

Hence, options (c) and (d) are correct.

Got questions? Get instant answers now!

The magnitude of centripetal acceleration is given by :

a v 2 r b ω 2 r c ω r d | ω X v |

The centripetal acceleration is given by :

a R = v 2 r

The linear speed "v" is related to angular speed by the relation,

v = ω r

Substituting this in the expression of centripetal acceleration, we have :

a R = ω 2 r 2 r = ω 2 r

We need to evaluate fourth cross product expression to know whether its modulus is equal to the magnitude of centripetal acceleration or not. Let the cross product be equal to a vector " A ". The magnitude of vector " A " is :

A = | ω X v | = ω v sin θ

For circular motion, the angle between linear and angular velocity is 90°. Hence,

A = | ω X v | = ω v sin 90 0 = ω v

Substituting for " ω", we have :

A = ω v = v 2 r

The modulus of the expression, therefore, is equal to the magnitude of centripetal acceleration.

Note : The vector cross product "| ω X v |” is the vector expression of centripetal force.

Hence, options (a) and (d) are correct.

Got questions? Get instant answers now!

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for k-12' conversation and receive update notifications?

Ask