Dynamics and Space 2 Flashcards
(24 cards)
Examples of motion in a circle:
Electrons in orbit around atoms
Washing machines
Theme park rides
Wheels
Motors
Angular velocity definition:
The rate of change of angular displacement.
How to convert a value from rpm to rad s^-1
Divide by 60 and multiply by 2PI
Angular acceleration definition:
The rate of change of angular velocity with respect to time.
Tangential velocity definition:
The velocity of the object in the direction of the tangent to the circle.
The tangential velocity ALWAYS points at 90 degrees to the radius of the circle.
How does the radius affect the tangential velocity.
Tangential velocity increases as the radius increases.
Which direction does the centripetal force act in?
Towards the centre of the curve/circle
Centripetal acceleration definition:
The rate at which an object’s velocity change direction towards the centre of the curve.
It does not affect the object’s speed but only its direction.
Slack meaning:
No tension
Taut meaning:
Always tension
At the midpoint of the circle:
Fc = R (or T)
At the top of the circle:
Fc = R + W
(W=mg)
At the bottom of the circle:
Fc = R - W
(W=mg)
Centripetal force at the top of a humped back bridge:
Fc = W - N
Where N is the normal force
We can calculate the velocity a car will leave the road at by setting N=0.
What happens if the centripetal force is removed from an object?
Initially, the object moves in a circular path because of the tension in the string pulling it towards the centre.
T=Fc
If the string is cut, T = 0, and
the object will carry on moving at the same speed and the same direction, tangentially (in a straight line)
How to calculate the maximum speed of a car cornering?
The friction between the wheels and the road provides the centripetal force, so:
Fc = Friction
If we know the friction we can calculate the max speed by rearranging the equations.
How can a vehicle take a corner on a frictionless banked track?
The horizontal component of the normal reaction force provides the required centripetal force.
How to calculate the speed of a car on frictionless banked tracks?
Draw a diagram of the normal reaction force (upwards and parallel to car on banked tracks), the weight (straight downwards), and the horizontal and vertical components of the normal reaction force.
The angle of the banked tracks is the same as the angle between the normal reaction force and its vertical component.
Horizontal forces: Rsin0 = (mv^2)/r
Vertical forces: Rcos0 = mg
Divide the horizontal forces by the vertical forces to get: tan0 = (v^2)/gr, then rearrange for v if needed.
How to calculate total Ek of a car rolling along a road?
Ek total = Ek translational + Ek rotational
Ek total = (1/2 x m x v^2) + (1/2 x I x w^2)
Conservation of angular momentum:
The total angular momentum before an event is equal to the total angular momentum after an event in the absence of all external torques.
How does a planet stay in orbit?
Gravitational attraction force provides the centripetal force.
What direction do field lines point?
In the direction a positive charge would follow.
How to combine gravitational fields?
To calculate the gravitational field strength at any point in the field due to two point masses or spheres, we take the vector sum of the two individual fields
