5.2 - Circular motion

Question 1

What are radians a unit of?

Answer 1

Angle

Question 2

How do you convert degrees to radians?

Answer 2

To convert an angle from degrees to radians, divide it by 360 and then multiply by 2π.

Question 3

What is meant by the period of an object in circular motion?

Answer 3

The time taken for one full rotation

Question 4

What is meant by angular velocity?

Answer 4

The angle travelled through divided by the time taken.
This is similar to linear speed, except we’re interested in rate of rotation rather than distance/time.

Question 5

What kind of force is required to keep an object moving in a circle at constant speed?

Answer 5

A constant centripetal force (a force applied always towards the centre of that circle).

Question 6

True or false: The centripetal force and velocity of an object moving in a circle are always in the same direction.

Answer 6

False.
Velocity is always at a tangent to the circle, force is always along a radius. They are perpendicular.

Question 7

How are linear and angular velocity related?

Answer 7

v = ⍵r

Where v = linear velocity, ⍵ = angular
velocity, and r = radius

Question 8

An object moving in a circle at a constant speed is not accelerating. True or False?

Answer 8

False.
The direction is always changing hence the velocity always changing which means it is accelerating.

Question 9

What equation gives acceleration in terms of angular velocity?

Answer 9

a=⍵²r

Question 10

What is acceleration in terms of linear velocity?

Answer 10

a = v²/r

Question 11

What are the equations for centripetal force?

Answer 11

F = mv²/r
or
F = m⍵²

Question 12

Describe the steps how one can investigate circular motion via an experiment

Answer 12

● Circular motion can be investigated experimentally by tying a bung, with mass m, to a piece of string, and threading it through a glass tube.
● The other end of the string has a weight, with mass M, suspended from it. This provides the centripetal force, F =Mg, as the tension throughout the string is constant.
● The string is whirled in a circle, and the time taken for a complete rotation is recorded.
● The mass of the weight is altered and the experiment repeated.
● We equate Mg and the centripetal force mv²/r so Mg=mv²/r
● By measuring the radius of the circle and using the time for one complete oscillation, the velocity can be determined. When v^2 is plotted against M, a straight line graph which passes through the origin should be produced