Week 9 - Angular Kinetics Torque

Question 1

Define torque

Answer 1

Tendency of a force to cause rotation, the turning effect produced by a force

Question 2

Torque equation

Answer 2

𝜏 = F * MA
OR
𝜏 = F * d

𝜏 = torque (Nm)
F = applied force (N)
MA or d = moment arm (m)

Question 3

What type of force is this?

Answer 3

Concentric force acting on the axis of rotation causing translation of the object

Question 4

What type of force is this?

Answer 4

An eccentric force acting outside the axis of rotation resulting in translation of the object and a clockwise torque

Question 5

What is a force couple

Answer 5

A pair of forces which are equal in magnitude, parallel and opposite in direction

Question 6

Define Intertia

Answer 6

Inertia is the law of universal laziness. Objects want to keep doing what they are already doing.

Question 7

Angular inertia depends on two things

Answer 7

Mass of the body AND how the mass is distributed with respect to the axis

Question 8

Define moment of inertia and what is the formula?

Answer 8

Sum of all mass particles multiplied by the radius squared

𝐼 = 𝑚𝑟2

I = moment of inertia (measured in kilogram metres squared (kg.m2 ))

m = sum of all particles masses (measured in kilograms (kg))

r = radius of gyration (m)

Question 9

Define RADIUS OF GYRATION (K)

Answer 9

Distance from the axis of rotation to a point where the body’s mass could be concentrated without altering its rotational characteristics (maximum mass located)

Question 10

Which bat is harder to swing and why?

Answer 10

Moment of intertia = mass x distance of mass from moment arm

The radius is the same, although the right bat has a greater mass

Question 11

Which bat will be harder to swing? and why?

Answer 11

They both have the same COM although the right is further to the axis, therefore being harder to swing

Question 12

Which person will have the greatest moment of inertia and why?

Answer 12

The one of the left, as the radius of the limbs is greater than the other three

Question 13

Why does a tightrope walker use a pole? 3 reasons

Answer 13

1. Increased weight = greater inertia = increased linear stability
2. Lower centre of mass = increased angular stability
3. Increased moment of intertia = increased resistance to rotation

Question 14

Newton’s first law for linear motion

Answer 14

A body will remain at rest or in constant motion unless acted upon by a net external force

Question 15

Newtons first law for angular motion

Answer 15

A rotating body will continue in a state of rest or constant angular moment unless acted upon by a net external torque

ΣT = 0

Question 16

Newton’s second law for angular motion

Answer 16

The rate of change of angular momentum of a body is proportional to the torque causing it AND the change takes place in the direction in which the torque acts.

ΣT = Iα

Question 17

Newton’s third law in angular motion

Answer 17

For every torque exerted by body A to body B, an equal and opposite torque is exerted by body B onto body A

ΣTA to B = -ΣTB to A

Question 18

Equation for angular momentum

Answer 18

𝑳 = 𝑰w

𝑳 = angular momentum

𝑰 = moment of inertia

w = angular velocity

Question 19

Consider a rotating body of 10kg for which the radius is 0.2m and the angular velocity is 3 rad/s.

What is the Angular Momentum?

𝑳 = 𝑰w

Answer 19

𝑳 = 𝑰w

L = (10 x 0.2squared) x 3

L = 1.2 kg.m2/s

Question 20

What causes a greater angular momentum? Increases the mass or radius?

Answer 20

Radius

Doubling the mass or velocity will double the angular momentum.

Doubling the radius, will quadruple the angular momentum.

Question 21

Conservation of Momentum

Answer 21

Any given system will continue to move with constant linear (translatory motion) or angular (rotating about an axis) momentum unless an external force (linear) or torque (angular) acts on the system to change the momentum

Question 22

If a diver doing a front roll decreases the moment of inertia what happens to the angular velocity?

Answer 22

It increases

Question 23

If a diver increases the moment of inertia what happens to angular momentum?

Answer 23

It decreases

Question 24

Impulse linear equation

Answer 24

Impulse = Ft

Ft = m(vf - vi)

Question 25

Impulse angular equation

Answer 25

impulse angular = T*t (torque x time)

T*t = I(wf - wi)