Define a radian
A radian is the angle subtended by a circular arc with a length equal to the radius of the circle.
State the equation to calculate radians
Radian = arc length/radius
Define time period
Time period (T) is the time taken for one complete revolution. It is measured in seconds (s)
Frequency is the number of revolutions per second. It is measured in Hertz (Hz)
Define linear velocity
Rate of change of displacement
measured in m/s
Define angular velocity
Rate of change of angle
measured in rad/s
angular velocity = Ø / t
State the relationship between linear velocity and angular velocity
linear velocity = angular velocity x radius
State the direction of centripetal force
Towards the centre of the circle
Define centripetal force
The overall resultant force acting towards the centre of a circle
State the direction of linear velocity
at a tangent to the circle and always at a right angle to the centripetal force
What is the angle between centripetal force and linear velocity
How can an object move at constant speed but still be accelerating?
if it is moving in a circular path it is constantly changing direction. That must means its velocity is constantly changing. A change in velocity means it is accelerating. It is always accelerating towards the centre of the circle.
State 3 factors that can increase the size of the centripetal force
- Bigger mass
- Faster velocity
- Smaller radius
Describe a practical to prove the relationship between linear velocity and centripetal force
- Use a bung attached to some string.
- Add masses to the end of the string to vary the centripetal force
- Swing the bung in a circular path and time for 10 revolutions.
- Calculate the velocity
- Keep the mass of the bung and radius of the circle constant, whilst varying the centripetal force by changing the number of masses.
- Plot a graph of centripetal force against velocity.
- To prove the relationship the graph should be a straight line that passes through the origin.
What causes the centripetal force for a planetary orbit
What causes the centripetal force for an electron in orbit
What causes the centripetal force for a bung on a string
What causes the centripetal force for a car cornering
What causes the centripetal force for a car cornering on a banked slope.
Normal reaction resolved horizontally and
friction resolved horizontally
What causes the centripetal force for an airplane banking
lift resolved horizontally
What causes the centripetal force for a rollercoaster at the top of a loop the loop
Reaction + weight
What causes the centripetal force for a rollercoaster at the bottom of a loop the loop
Reaction - weight
Why is the normal reaction for a rollercoaster greater at the bottom of a loop the loop that at the top
At the top the weigh helps contribute to the centripetal force.
At the bottom the reaction force has to overcome all the weight and then provide the centripetal force.
In the rotor/gravitron ride what forces are acting
Vertical equilibrium where weight is balanced by friction.
Horizontally its accelerating with normal reaction providing the centripetal force.
What cause the centripetal force on a pirate ship?
T - mg cos Ø
What causes the centripetal force on the swing o chairs?
Tension resolved horizontally