Rotational Dynamics

Question 1

An unbalanced torque causes a change in the

Answer 1

angular rotational motion of an object

Question 2

definition of moment of inertia

Answer 2

moment of inertia of an object as a measure of its resistance to angular acceleration about a given axis

Question 3

moment of inertia depends on

Answer 3

mass and the distribution of mass about a given axis of rotation

Question 4

I = mr^2

point mass

Answer 4

I = moment of inertia (kg m^2)
m = mass
r = distance from centre of axis of rotation to point mass

Question 5

Moment of inertia = I

Answer 5

measured in kg m^2

Question 6

I = 1/12ml^2

rod about a centre
where the centre of the rod is at the centre of the axis of rotation

Answer 6

I = moment of inertia (kg m^2)
m = mass (kg)
l = length of rod (m)

Question 7

I = 1/3ml^2

rod about end
where the end of the rod is at the centre of the axis of rotation

Answer 7

I = moment of inertia (kg m^2)
m = mass (kg)
l = length of rod (m)

Question 8

I = 1/2mr^2

disc about centre
a 3d disc, unlike the point mass which is flat.

Answer 8

I = moment of inertia (kg m^2)
m = mass (kg)
r = distance from end of disc to centre of axis of rotation

Question 9

I = 2/5mr^2

sphere about centre

Answer 9

I = moment of inertia (kg m^2)
m = mass (kg)
r = radius of the sphere, distance from centre of axis of rotation to edge of sphere

Question 10

Torque

T

Answer 10

(N m)

Question 11

Torque

T = Fr

Answer 11

T = Torque (N m)
F = Force (N)
r = perpendicular distance between direction of force and axis of rotation (m)

Question 12

If the force is not applied perpendicular i.e an angle of 15 degrees then its perpendicular component would have to be calculated by

Answer 12

T = Fr
T = sin15 x r
T = 0.65r

Question 13

An unbalanced Torque will produce an angular acceleration about an axis of rotation

Tᵤₙ = Iα

Answer 13

Tᵤₙ = Unbalanced Torque (N m)
I = Moment of inerti (kg m^2)
α = angular acceleration (rad s-2)

Question 14

Angular Momentum

L

Answer 14

kg m^2 s-1

Question 15

L = mvr
L= mr^2w
L=Iw

Answer 15

L = angular momentum (kg m^2 s-1)
m = mass (kg)
v = linear velocity (ms-1)
r = radius (m)
I = moment of inertia (kg m^2)
w = angular velocity (rad s-1)

Question 16

The principle of conservation of angular momentum

Answer 16

Total angular momentum before = Total angular momentum after

Question 17

The conservation of angular momentum formula

Not in data book!

Answer 17

I₁w₁= I₂w₂

Just as linear momentum is conserved when two or more objects collide in absence of external forces

I = moment of inertia (kg m^2)
w = angular velocity (rad s-1)

Question 18

when combining different objects use this formula

I = Σmr^2

The sum of moment of inertia , add them together

Answer 18

Moment of inertia = the sum of the mr^2

find their I then add them together

Question 19

Rotational Kinetic Energy

Ek = 1/2Iw^2

Answer 19

Ek + kinetic energy of a rotating body (J)
I = moment of inertia (kg m^2)
w = angular velocity (kg m^2)

Question 20

Ep = Ek (linear) + Ek (rotational)

so

Answer 20

mgh = 1/2mv^2 +1/2lw^2

Question 21

worked example of rotational kinetic energy

Answer 21

Ep lost = Ek gained
mgh = 1/2mv^2 + 1/2lw^2
since w = v/r
mgh = 1/2mv^2 + 1/2l x (v^2/r^2)
take v^2 out both leaving as a fraction (1/r^2)
mgh = v^2 (1/2m + 1/2l x (1/r^2)

this is now solvable with numerical values.

Question 22

Ep lost =

Answer 22

Ek gained

Question 23

Why does an object no longer travel in a circular path when the speed is reduced

Answer 23

Tension will be reduced

Weight is bigger than the centripetal force

Question 24

An object at its highest point about its rotation of axis will have the equation

Answer 24

Fᵤₙ = Tension + Weight

Both weight and tension are in the downward direction towards the centre of the axis

Question 25

An object at its lowest point about its rotation of axis will have the equation

Answer 25

Fᵤₙ = Tension - Weight

Tension is in the upward direction towards the centre of the axis and weight is in the downwards direction

Question 26

the moment of inertia has decreased when a person pulls there legs in why?

Answer 26

the distribution of mass is closer to the AXIS of ROTATION!

Question 27

a solid cylinder has the same moment of inertia as what

Answer 27

as a disc

I = 1/2mr^2

Question 28

why would there be a decrease in moment of inertia between two different moments of inertia experiments involving kinetic energy?

Answer 28

Energy is lost

Question 29

a cube has the same moment inertia as what

Answer 29

as a disc

I = 1/2mr^2

Question 30

if an object is denser then the moment of inertia is

Answer 30

greater and thus the speed of the mass will be less