Module 5 Circular Motion

Question 1

Define a radian.

State formulae to calculate radian in terms of the arc length and radius.

Answer 1

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

Question 2

Define period of circular motion.

Answer 2

It is the time taken in seconds to complete one rotation

Question 3

Does the formula theta=c/r calculate the angle in pi radians?
What is 35 radians in pi radians?

Answer 3

Only if the values inserted are in terms of pi.

35/pi = 11.1pi radians

Question 4

Show that 2pi radians = 360 degrees, if 1 radian = 57.3 degrees.

Answer 4

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

Question 5

How do you convert from radians to degrees and vice versa?

Answer 5

Radians to degrees:
(Angle x 360)/2pi

Degrees to radian:
Angle x 2pi/360

Question 6

What is the formula for angular velocity and what is it’s symbol?

Answer 6

Angular velocity = w

w=2 pi/T

Question 7

What is si unit of angular velocity?

Answer 7

rad/s

Question 8

How do you calculate linear velocity “v” in a circle?

Derive the relation between “v” and “w”.

Answer 8

v=2Pi r/T

Since w=2 pi/T

v=w x r

Question 9

Relate linear velocity and frequency.

Answer 9

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

Question 10

Define centripetal acceleration.

Answer 10

It is the acceleration of a body undergoing circular motion with a constant linear speed.

Question 11

State the formula for calculating centripetal acceleration.

Answer 11

a=v^2/r

Question 12

Relate centripetal acceleration to “w”

Answer 12

a=v^2/r

Since v=wr

a=(wr)^2/r
a=w^2xr

Question 13

Define centripetal force.

Answer 13

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.

Question 14

State formula for centripetal force in terms of v and w

Answer 14

F=mv^2/r

v= wr

F=m x (wr)^2/r = mw^2r

Question 15

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?

Answer 15

It compliments the force.

F= mv^2/r + mg.

Question 16

Does weight do any work on a body and hence cause acceleration if the body is rotating horizontally?

Answer 16

No work is done as weight is acting perpendicular to the direction of motion. No acceleration due to weight.

Question 17

What is the major difficulty in a pendulum pag and how do you overcome it?

Answer 17

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.