Rotational dynamics Flashcards

1
Q

What is inertia?

A

The resistance to a change of motion in linear motion
The larger the mass of an object, the greater the inertia

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2
Q

What is the moment of inertia?

A

The rotational equivilant of inertia for linear motion
The resistance to a change of rotational motion, depending on the distribution of mass around a chosen axis of rotation

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3
Q

What does the moment of inertia measure?

A

How ‘easy’ or ‘hard’ it is to rotate an object

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4
Q

How do you calculate moment of inertia when a system has more than one component rotating the same axis?

A

We calculate the moment of inertia of each individual component seperately, using their individual mass and radius, and then add it together for the overall moment of inertia

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5
Q

How do you calculate moment of inertia?

A

Moment of inertia = mass x radius^2

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6
Q

Why do we need moment of inertia?

A

The moment of inertia in rotational dynamics plays the same roll as mass in linear motion
Instead of using mass in equations, we use moment of inertia

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7
Q

What is rotational kinetic energy?

A

A body moving with linear motion has an associated linear kinetic energy. Similarily, a rotating object has an associated rotational kinetic energy

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8
Q

How do you calculate rotational kinetic energy?

A

It is given by its moment of inertia (in place for mass) and angular velocity (in place for velocity)
Rotational kinetic energy = 1/2 x moment of inertia x angular velocity^2

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9
Q

What is rolling motion?

A

Circular objects are made to move with both linear and rotational motion
Rolling motion is a combination of rotating and sliding (tranational) motion

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10
Q

How does angular and linear velocity differ as a disc rotates?

A

Each point on the disc has a different angular velocity depending on its distance from the centre
The linear velocity is the same at all points on the circumference

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11
Q

What happens when a disc rolls without sliping?

A

There is enough friction present to initiate rotational motion
The point in contact with the surface has a velocity of 0
The centre of mass has a velocity of angular velocity x radius
The top point has a velocity of angular velocity x radius^2

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12
Q

What happens to GPE when rolling down a slope?

A

As the object rolls down the slope, the gravitational potential energy is transferred to both the linear (translational) kinetic energy and rotational kinetic energy as 2 seperate stores

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13
Q

What is angular displacement?

A

The change in angle (radians) through which a rigid body has rotated relative from point A to point B

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14
Q

What is angular velocity?

A

The rate of change of angular displacement, with respect to time

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15
Q

What is angular acceleration?

A

The rate of change of angular velocity, with respect to time

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16
Q

How do you calculate angular displacement, angular velocity and angular acceleration?

A

AD: θ (radians)
AV: ω = θ / ∆t
AA: α = ∆ω / ∆t

17
Q

Angular equivalents for linear variables

A

s = θ (displacement)
u = ωi (initial velocity)
v = ωf (final velocity)
a = α (acceleration)
t = t (time)

18
Q

Uniform angular acceleration equations

A

The linear acceleration equations (suvat) can be swapped out for their angular equivalents to get the angular acceleration equations
ωf = ωi + αt

19
Q

What is torque?

A

Torque is the change in rotational motion due to a turning force
Torque = applied force x perpendicular distance from axis
T (Nm) = F (N) x r (m)

20
Q

What is the torque of a couple?

A

The sum of the moments produced by each of the forces in the moment

21
Q

Why does a net force of a couple?

A

The forces in a couple are equal and opposite hence do not produce a resultant force
Due to Newton’s second law, no resultant force means a couple won’t cause an object to accelerate, it will only rotate with a constant angular velocity

22
Q

Newton’s second law in rotational dynamics

A

The torque required to give a rotating object a certain angular acceleration is calculated using T = Iα (F=ma)

23
Q

What is the difference between T = Iα and T = Fr

A

T = Fr : how much torque a force produces
T = Iα : how that torque changes the rotation of the object

24
Q

How do you calculate angular momentum?

A

Angular momentum = moment of inertia x angular velocity
L = Iω

25
Conservation of angular momentum
A system always remains constant unless a net torque is acting on the system An increase in radius results in an increase in moment of inertia hence, a decrease in angular velocity
26
What is angular impulse?
An average resultant torque acting for a certain amount of time Change in angular momentum
27
How do you calculate angular impulse?
∆L = T∆t = ∆(Iω)
28
What is rotational work done and how do you calculate it?
Work must be done on an object to make it rotate a certain distance Work done (J) = torque (Nm) x angular displacement (rad/s) W = Tθ
29
How does work done relate to kinetic energy?
Work done can also be calculated by change in rotational kinetic energy Final rotational kinetic energy - initial rotational kinetic energy
30
What is frictional torque?
The difference between the applied torque and the resulting net torque
31
How do you calculate frictional torque?
Frictional force x radius Moment of inertia x average deceleration
32
Why do we minimise frictional torque?
To minimise the kinetic energy that is lost to heat and sound
33
What is power?
Rate of energy transfer Rate of doing work
34
How do we calculate rotational power?
Power (watts) = torque (Nm) x angular valocity (rad/s) P = W / t = Tθ / t = Tω