Further Mechanics

Question 1

angular displacement

Answer 1

The angle travelled by an object in circular motion

Question 2

angular speed

Answer 2

The angle an object rotates through (angular displacement) per second; the magnitude of angular velocity

Question 3

angular velocity

Answer 3

The angle an object rotates through (angular displacement) per second in a certain direction around a certain axis

Question 4

radian formula for circular motion

Answer 4

= arc length divided by the radius of the
circle = l / r

Question 5

1 radian

Answer 5

The angle travelled by an object in circular motion by an arc that is equal in length to the radius.

Question 6

time period for circular motion

Answer 6

The time taken for one complete revolution (i.e. one circular rotation)

Question 7

linear/orbital speed

Answer 7

The distance an object covers per unit time in circular motion (direction = tangent); how fast an object would be travelling in a straight line if it broke off from circular motion.

Question 8

A point on the Earth’s equator completes a full circle in ____.

Answer 8

24 hours

Question 9

The Earth rotates on its axis once each day. Explain any differences in its linear speed.

Answer 9

ang speed = v / r

The angular speed is constant, but the value for linear speed (v) at any particular point on the Earth’s surface depends on the radius of the circle.

So points at different latitudes (different displacements from the equator) have different radii, so have different values for linear speed - the speed at the equator being the greatest.
Note: consider the relative speeds of points closer and further from the equator. Areas near the pole barely move whereas areas near the equator have to travel much further in the day and so travel faster.

Question 10

You’re given a question about the Earth rotating on its axis. What should you always think about?

Answer 10

angular speed -> considering T = 1 day and the distance travelled in one revolution = 2 pi