Abeka Physics Section 13.1 pg. 186 - 192

Question 1

Define angular motion and give the two types of angular motion

Answer 1

> angular motion - any body or particle moving around an axis, or center of rotation
two types of angular motion: circular motion and rotary motion

Question 2

Distinguish between circular motion and rotary motion

Answer 2

> circular motion describes particle orbiting external axis, like planets orbiting the sun
rotary motion is exhibited by the sun because it spins on its own internal axis

Question 3

Define arc length

Answer 3

> arc length - linear distance from one point to another on circular path
symbolized “s”

Question 4

Define and describe rim speed

Answer 4

> rim speed - linear speed of a point on the rim of a rotating body
for given body in rotation, rim speed is greater than the speed of any internal point
linear speed of point on axis of rotation is zero

Question 5

Define radian

Answer 5

> one radian is measure of an angle that, when its vertex is set upon the center of a circle, subtends an arc equal in length to the radius of that circle

Question 6

What are the conversions among radians, revolutions, and degrees?

Answer 6

> 1 revolution = 2pi radians = 360 degrees

Question 7

Solve this: Perform the following conversions: (a) 1.0 degrees to radians, (b) 35.0 degrees to revolutions, (c) 1.5pi rad to degrees, (d) 2.70 rev to radians.

Answer 7

(a) (1.0 degrees) (pi rad/180degrees) = 0.017 rad
(b) (35.0degrees) (1 rev/360degrees) = 0.0972 rev
(c) (1.5pi rad) (180degrees/pi rad) = 270 degrees
(d) (2.70 rev) (2pi rad/1 rev) = 17.0 rad

Question 8

Define and describe angular displacement

Answer 8

> angular displacement - change in angular position (on the circumference of a circle) or radian measure of the angle through which the body turns
amount of rotation accomplished by a rotating body is measured as angular displacement
general rule: angular displacement (in radians) of body is length of arc traced by single point on rim divided by length of radius
is dimensionless number
theta(sub rad) = s / r where s is length of arc and r is length of radius

Question 9

Define and describe angular velocity

Answer 9

> angular velocity - change in angular displacement per unit time of a rotating body
whether or not angular velocity of body is constant throughout interval, body may be considered to have average angular velocity, given by
omega(sub av) = theta(sub rad) / t where omega(sub av) is average angular velocity measured in rad/s

Question 10

Solve this: A merry-go-round turns at a constant speed of 8.00 revolutions per minute (rpm) for 5.00 min. (a) Find the total angular displacement in radians. (b) Find the angular velocity in rad/s.

Answer 10

(a) If the speed is 8.00 rpm, in 5.00 min the merry-go-round goes through
(8.00 rev/min)(5.00 min) = 40.0 rev
Since there are 2pi rad in one revolution, the total angular displacement is
theta(sub rad) = (40.0rev)(2pi rad/1 rev)
theta(sub rad) = 251.32… rad = 251 rad

(b)First, convert 5.00min into 300.s. Then, substitute the answer from (a) into equation
omega(sub av) = theta(sub rad) / t and solve.
omega(sub av) = 251.32…rad / 300.s
omega(sub av) = 0.838 rad/s

Question 11

Define and describe angular acceleration

Answer 11

> angular acceleration - change in angular velocity

>