Rotational Motion and Astrophysics Flashcards
Explain the difference between angular, tangential and centripetal acceleration.
- Angular acceleration is the rate of change of angular velocity
- Tangential acceleration is the rate of change of tangential speed
- Centripetal acceleration is the rate of change of tangential velocity- this causes the direction of the object to change and results in circular motion.
How would you find the instantaneous velocity of an object from a displacement-time graph such as this?
Take the gradient of the line.
If the graph is a curve, take the gradient of the tangent to the curve at a point.
How would you find the instantaneous acceleration of an object from a velocity-time graph such as this?
Take the gradient of the line.
If the graph is a curve, take the gradient of the tangent to the curve at a point.
How would you find the displacement of an object from a velocity-time graph such as this?
Calculate the area underneath the graph- remember to include negative values.
If the graph is a curve, the equation of the graph can be integrated to get an expression for displacement.
How would you convert an angle from degrees into radians?
Angle in radians = (2π/360) x Angle in degrees
What relationships would you use to convert between:
- Linear displacement and angular dispalcement
- Linear velocity and angular velocity
- Linear acceleration and angular acceleration
For any of these relationships, you would multiply the angular quantity by the radius of circular motion to get the linear quantity:
How is angular velocity defined in terms of angular dispalcement?
Angular velocity is defined as the rate of change of angular displacement:
How is angular acceleration defined in terms of angular velocity?
Angular acceleration is defined as the rate of change of angular velocity.
What is meant by Torque (sometimes called the moment of a force)?
Torque is the turning effect of a force on a rotating object.
What is meant by the moment of inertia of an object?
The moment of inertia of an object is a measure of its resistance to angular acceleration about a given axis.
State the law of conservation of angular momentum.
In the absence of external torques, the total angular momentum of object(s) before a collision is equal to the total angular momentum of the object(s) after the collsion.
Which two quantities does the rotatinal kinetic energy of an object depend on?
Moment of Inertia and angular velocity
What is the definition of the gravitational field strength at a point?
The force exerted per unit mass (by a gravitational field).
What is the definition of gravitational potential at a point in space?
The work done in moving a unit mass from infinity to that point in space.
At which point do both gravitational potential and gravitational potential energy have values of zero?
They both have values of zero at infinity
What is the definition of escape velocity?
The minimum velocity required to allow a mass to escape a gravitational field (and have zero gravitational potential energy)
or
The minimum velocity required to allow a mass to reach infinity
By referring to ‘frames of reference’, in which situations would
a) Special relativity
and
b) General relativity
apply?
a) Special relativity deals with motion in inertial (non-accelerating) frames of reference.
b) General relativity deals with motion in non-interial (acceelrating) frames of reference.
State what is meant by the ‘equivalence principle’.
It is impossible to tell the difference
between the effects of a uniform gravitational field and
of a constant acceleration.
Describe the effect of placing a clock at a higher altitude in a gravitational field.
The clock would run faster higher in a gravitational field.
On a spacetime diagram, what is the name given to lines representing an object’s motion?
World-lines
Describe the effect of placing a clock at a lower altitude in a gravitational field.
The clock would run slower lower in a gravitational field.
The world-lines on the following space time diagram represent the motion of different objects, A, B and C.
Describe the motion of objects A, B and C.
Object A is stationary
Object B is moving with a constant velocity
Object C is accelerating
Light or freely moving objects under the influence of gravity follow particular paths in spacetime. What are these paths called?
Geodesics