Rotational Motion Flashcards
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 relationships would you use to convert between:
- Linear displacement and angular displacement
- 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:
What does the prefix f stand for?
f = femto = x 10-15
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.
Which two things does the moment of inertia of an object depend on?
- The mass of the object
- The distribution of mass around a given axis of rotation (which can be quantified with the radius, r)
What does the prefix M stand for?
M = mega = x 106
What is the unit of angular displacement?
Radians (rad)
[note: rads is incorrect]
What does the prefix G stand for?
G = giga = x 109
What does the prefix m stand for?
m = milli = x 10-3
How is angular acceleration defined in terms of angular velocity?
Angular acceleration is defined as the rate of change of angular velocity.
What is the unit of moment of inertia?
kg m2
What does the prefix p stand for?
p = pico = x 10-12
How is angular velocity defined in terms of angular displacement?
Angular velocity is defined as the rate of change of angular displacement:
What is the unit of Torque?
newton-metres (Nm)
What is the unit of angular acceleration?
rad s-2
What does the prefix k stand for?
k = kilo = x 103
What does the prefix P stand for?
P = peta = x 1015
What is the unit of centripetal acceleration?
ms-2
What is the unit of angular velocity?
rad s-1
Convert 360° into radians.
360° = 2π radians = 6.28 rad
The following experimental setup can be used to determine the moment of inertia of a disc which is allowed to rotate on a frictionless air bearing turntable.
Explain the measurements which will need to be taken, and how to use these to determine the moment of inertia of the disc.
Find the torque applied to the disc by using the relationship T = Fr.
Use the light gate to measure the angular acceleration of the disc.
Vary the hanging mass to vary the torque, and repeat a few times.
Plot T against α, and take the gradient of the straight line which will be equal to the moment of inertia of the disc.
What is the definition of 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.
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.
Which two quantities does the rotational kinetic energy of an object depend on?
Moment of Inertia and angular velocity
What does the prefix T stand for?
T= tera = x 1012
What is the unit of angular momentum?
kilogram metres squared per second
(kg m2 s-1)
(kg m2 rad s-1 also acceptable)
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.
What does the prefix µ stand for?
µ = micro = x 10-6
A ‘conical pendulum’ is shown below.
In terms of the components of tension in the string determine expressions for the:
- Centripetal force
- Weight of the ‘bob’.
- Centripetal force = T sinθ
- Weight = T cosθ
In a ‘loop the loop’ ride at a funfair, how would you determine the minimum speed required to complete a full loop?
The minimum speed required is when there is no reaction force acting on the ‘car’, so.
Centripetal force = Weight + Reaction force
simplifies to
Centripetal force = Weight
mv2/r = mg
v = √gr
An ice skater is spinning with his arms outward as shown.
He then pulls his arms inward.
Explain what happens to his angular momentum and rotational kinetic energy.
Angular momentum constant because angular momentum is always conserved
Rotational kinetic energy increases because angular velocity increases.
What is the unit of tangential acceleration?
ms-2
A ball of weight W attached to a string is ‘whirling’ in a horizontal circle as shown below.
What provides the centripetal force acting on the ball?
The centripetal force is suppled by the tension, T only.
T is the only force acting into the centre.
A ball of weight W attached to a string under tension T is ‘whirling’ in a vertical circle as shown below.
Determine a relationship for the centripetal force acting on the ball:
- at the bottom.
- at the sides.
- at the top.
- Centripetal force = Tension - Weight
- Centripetal force = Tension
- Centripetal force = Tension + Weight
An expression for the displacement of an object with respect to time is given as
s = 3.1t2 + 4.1t + 6
Determine expressions for the object’s velocity and acceleration.
v = 6.2t + 4.1
a = 6.2 (ms-2)
Describe how to convert an angular velocity in rpm (revolutions per minute) into rad s-1 (radians per second).
revolutions per minute → radians per second:
× 2π then ÷ 60
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 collision.
What does the prefix n stand for?
n = nano = x 10-9
Convert 15 revolutions into radians.
15 revolutions = 30π radians = 94.2 rad
