AH 1.2 Angular Motion Flashcards
Explain what is meant by angular displacement (angle) by drawing a diagram and stating an equation.
Define all symbols used and specify units.
State, in words, what is meant by angular velocity
Angular velocity is the rate of change of angular displacement.
Write down the equation for angular velocity of a particle P describing uniform circular motion specifying all symbols and naming units.
Anglular velocity unit: radians per second
Angular displacemnt unit: radians
Time unit: seconds
Write down the equation for instantaneous angular velocity.
Write down the equation for instantaneous angular acceleration in terms of
anglular velocity and
angular displacement.
Copy and complete the table to show the angular versions of the linear equations of motion.
Derive the equation given below for the linear (tangential) velocity of a body describing uniform circular motion.
Derive the equation for the tangential linear acceleration of a body describing non-uniform circular motion.
What condition must always be met for a body to describe iniform circular motion?
The body must be subjecy to a centrally directed i.e. centripetal force.
Is a centripetal force always balanced or unbalanced?
Centripetal force always unbalanced.
How is it possible for a body describing uniform circular motion to be accelerating whilst maintaining a constant linear speed?
Velocity is a vector quantity. Although the magnitude of the (linear) velocity is uniform, it’s direction is contstantly changing, as the object concerned is moving in a circle.
Derive the equations for centripetal (i.e radial) acceleration given below.
Study the information below then write down two equations for centripetal force. These follow directly from the equations for centripetal acceleration.
A bucket of water on the end of a string is swung by a pupil in a vertical circle anticlockwise as you view it. This is showb below in the diagram.
Draw a digram showing all forces acting on the water at the following postions during the circular swing:
1) The top of the swing (12 o’clock position)
2) The bottom of the swing (6 o’clock position)
3) Half way up (3 o’clock position)
4) Half way down (9 o’clock position)
A car of mass 800 kg travels at 20 ms-1 round a circular road of radius 100m exhibit uniform circular motion.
Q1 What force causes the circular motion?
Q2 Find the size of this frictional force.
A1 A centrally directed Frictional force by the road on the tyres.
A2. mv2/r = f
f = 800 x (202) / 100
f = 3 200 N
With the aid of a diagram, show that the linear speed v of a car describing uniform circular motion, radiud r, around a banked track, angle ø to the horizontal, is given by
v2 = gr tan ø
What does this equation tell youy about the relationship between the angle of the track and the speed the car can go at in safely rounding the bend?
Show that, for a car travelling at a uniform velocity v over a semi-circular arched bridge, radius r,
v = ⎷gr
By sketching a concial pendulum and analysing the forces on the bob, show that the anlge ø of the pendulum string to the vertical is given by
tan ø = v2/gr
