<< Chapter < Page Chapter >> Page >
The given figure shows the top view of an old fashioned vinyl record. Two perpendicular line segments are drawn through the center of the circular record, one vertically upward and one horizontal to the right side. Two flies are shown at the end points of the vertical lines near the borders of the record. Two arrows are also drawn perpendicularly rightward through the end points of these vertical lines depicting linear velocities. A curved arrow is also drawn at the center circular part of the record which shows the angular velocity.
As an object moves in a circle, here a fly on the edge of an old-fashioned vinyl record, its instantaneous velocity is always tangent to the circle. The direction of the angular velocity is clockwise in this case.

Phet explorations: ladybug revolution

Ladybug Revolution

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.

Section summary

  • Uniform circular motion is motion in a circle at constant speed. The rotation angle Δ θ size 12{Δθ} {} is defined as the ratio of the arc length to the radius of curvature:
    Δ θ = Δ s r , size 12{Δθ= { {Δs} over {r} } ","} {}

    where arc length Δ s size 12{Δs} {} is distance traveled along a circular path and r size 12{r} {} is the radius of curvature of the circular path. The quantity Δ θ size 12{Δθ} {} is measured in units of radians (rad), for which

    rad = 360º 1  revolution. size 12{2π`"rad"=`"360""°="`1`"revolution."} {}
  • The conversion between radians and degrees is 1 rad = 57 . 3 º size 12{1"rad"="57" "." 3°} {} .
  • Angular velocity ω size 12{ω} {} is the rate of change of an angle,
    ω = Δ θ Δ t , size 12{ω= { {Δθ} over {Δt} } ","} {}

    where a rotation Δ θ size 12{Δθ} {} takes place in a time Δ t size 12{Δt} {} . The units of angular velocity are radians per second (rad/s). Linear velocity v size 12{v} {} and angular velocity ω size 12{ω} {} are related by

    v =  or  ω = v r . size 12{v=rω``"or "ω= { {v} over {r} } "."} {}

Conceptual questions

There is an analogy between rotational and linear physical quantities. What rotational quantities are analogous to distance and velocity?

Got questions? Get instant answers now!

Problem exercises

Semi-trailer trucks have an odometer on one hub of a trailer wheel. The hub is weighted so that it does not rotate, but it contains gears to count the number of wheel revolutions—it then calculates the distance traveled. If the wheel has a 1.15 m diameter and goes through 200,000 rotations, how many kilometers should the odometer read?

723 km

Got questions? Get instant answers now!

Microwave ovens rotate at a rate of about 6 rev/min. What is this in revolutions per second? What is the angular velocity in radians per second?

Got questions? Get instant answers now!

An automobile with 0.260 m radius tires travels 80,000 km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?

5 × 10 7 rotations size 12{9 "." "79" times "10" rSup { size 8{8} } `"rotations"} {}

Got questions? Get instant answers now!

(a) What is the period of rotation of Earth in seconds? (b) What is the angular velocity of Earth? (c) Given that Earth has a radius of 6 . 4 × 10 6 m size 12{6 "." 4 times "10" rSup { size 8{6} } } {} at its equator, what is the linear velocity at Earth’s surface?

Got questions? Get instant answers now!

A baseball pitcher brings his arm forward during a pitch, rotating the forearm about the elbow. If the velocity of the ball in the pitcher’s hand is 35.0 m/s and the ball is 0.300 m from the elbow joint, what is the angular velocity of the forearm?

117 rad/s

Got questions? Get instant answers now!

In lacrosse, a ball is thrown from a net on the end of a stick by rotating the stick and forearm about the elbow. If the angular velocity of the ball about the elbow joint is 30.0 rad/s and the ball is 1.30 m from the elbow joint, what is the velocity of the ball?

Got questions? Get instant answers now!

A truck with 0.420-m-radius tires travels at 32.0 m/s. What is the angular velocity of the rotating tires in radians per second? What is this in rev/min?

76.2 rad/s

728 rpm

Got questions? Get instant answers now!

Integrated Concepts When kicking a football, the kicker rotates his leg about the hip joint.

(a) If the velocity of the tip of the kicker’s shoe is 35.0 m/s and the hip joint is 1.05 m from the tip of the shoe, what is the shoe tip’s angular velocity?

(b) The shoe is in contact with the initially stationary 0.500 kg football for 20.0 ms. What average force is exerted on the football to give it a velocity of 20.0 m/s?

(c) Find the maximum range of the football, neglecting air resistance.

(a) 33.3 rad/s

(b) 500 N

(c) 40.8 m

Got questions? Get instant answers now!

Construct Your Own Problem

Consider an amusement park ride in which participants are rotated about a vertical axis in a cylinder with vertical walls. Once the angular velocity reaches its full value, the floor drops away and friction between the walls and the riders prevents them from sliding down. Construct a problem in which you calculate the necessary angular velocity that assures the riders will not slide down the wall. Include a free body diagram of a single rider. Among the variables to consider are the radius of the cylinder and the coefficients of friction between the riders’ clothing and the wall.

Got questions? Get instant answers now!

Questions & Answers

a diagram of an adult mosquito
mubarak Reply
what are white blood cells
Mlungisi Reply
white blood cell is part of the immune system. that help fight the infection.
MG
what about tissue celss
Mlungisi
Cells with a similar function, form a tissue. For example the nervous tissue is composed by cells:neurons and glia cells. Muscle tissue, is composed by different cells.
Anastasiya
I need further explanation coz celewi anything guys,,,
Calvin Reply
hey guys
Isala
on what?
Anastasiya
is air homogenous or hetrogenous
damiane Reply
homogenous
Kevin
why saying homogenous?
Isala
explain if oxygen is necessary for photosynthesis
Allice Reply
explain if oxygen is necessary for photosynthesis
Allice Reply
Yes, the plant does need oxygen. The plant uses oxygen, water, light, and produced food. The plant use process called photosynthesis.
MG
By using the energy of sunlight, plants convert carbon dioxide and water into carbohydrates and oxygen by photosynthesis. This happens during the day and sunlight is needed.
NOBLE
no. it s a product of the process
Anastasiya
yet still is it needed?
NOBLE
no. The reaction is: 6CO2+6H20+ solar energy =C6H12O6(glucose)+602. The plant requires Carbon dioxyde, light, and water Only, and produces glucose and oxygen( which is a waste).
Anastasiya
what was the question
NOBLE Reply
joining
Godfrey
the specific one
NOBLE
the study of non and living organism is called.
Godfrey
Is call biology
Alohan
yeah
NOBLE
yes
Usher
what Is ecology
Musonda Reply
what is a cell
Emmanuel Reply
A cell is a basic structure and functional unit of life
Ndongya
what is biolgy
Hawwi Reply
is the study of living and non living organisms
Ahmed
may u draw the female organ
MARTIN Reply
i dont understand
Asal
:/
Asal
me too
DAVID
anabolism and catabolism
Sani Reply
Anabolism refers to the process in methabolism in which complex molecules are formed "built" and requires energy to happen. Catabolism is the opposite process: complex molecules are deconstructed releasing energy, such as during glicolysis.
Anastasiya
Explain briefly independent assortment gene .
Otu Reply
hi
Amargo
hi I'm Anatalia
Joy
what do you mean by pituitary gland
Digambar
draw and lable the cell
Ameh Reply
why homones are destroyed soon after completing their role
Nyirenda Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 6

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask