Module 5 Circular Motion Flashcards
Define a radian.
State formulae to calculate radian in terms of the arc length and radius.
It is the angle subtended at the centre of a circle when the arc length is equal to the radius of the circle.
Theta=arc length/radius
Define period of circular motion.
It is the time taken in seconds to complete one rotation
Does the formula theta=c/r calculate the angle in pi radians?
What is 35 radians in pi radians?
Only if the values inserted are in terms of pi.
35/pi = 11.1pi radians
Show that 2pi radians = 360 degrees, if 1 radian = 57.3 degrees.
1 radian/ pi = 0.318 pi radian
0.318 pi radian = 57.3 degrees
360/57.3=x/0.318 pi radian
x = 360 x 0.318 pi radian/57.3
x=1.997 ~ 2 pi radians
How do you convert from radians to degrees and vice versa?
Radians to degrees:
(Angle x 360)/2pi
Degrees to radian:
Angle x 2pi/360
What is the formula for angular velocity and what is it’s symbol?
Angular velocity = w
w=2 pi/T
What is si unit of angular velocity?
rad/s
How do you calculate linear velocity “v” in a circle?
Derive the relation between “v” and “w”.
v=2Pi r/T
Since w=2 pi/T
v=w x r
Relate linear velocity and frequency.
v = w x r
w= 2 pi/T
f=1/T
w=2 pi/1/T = 2 pi x f
v=2 pi x f x r
Define centripetal acceleration.
It is the acceleration of a body undergoing circular motion with a constant linear speed.
State the formula for calculating centripetal acceleration.
a=v^2/r
Relate centripetal acceleration to “w”
a=v^2/r
Since v=wr
a=(wr)^2/r
a=w^2xr
Define centripetal force.
It is the resultant force acting perpendicular to the linear speed of a body towards the centre of the circle, causing it to move in a circular path.
State formula for centripetal force in terms of v and w
F=mv^2/r
v= wr
F=m x (wr)^2/r = mw^2r
During circular motion in the vertical plane, does the weight of a body compliment or oppose the centripetal force at the highest vertical point?
How do you calculate centripetal force in this scenario?
It compliments the force.
F= mv^2/r + mg.
Does weight do any work on a body and hence cause acceleration if the body is rotating horizontally?
No work is done as weight is acting perpendicular to the direction of motion. No acceleration due to weight.
What is the major difficulty in a pendulum pag and how do you overcome it?
The angle of swing decreases during oscillation.
You can measure the time taken for 1/4 the oscillation using a data logger or video camera.
