Angular Kinematics

Question 1

What is kinematics?

Answer 1

• description of motion
• geometry of motion
• “what” happened

Question 2

What is angular kinematics?

Answer 2

• motion of a body (person or object) or body part around a fixed axis through an angle of X number of degrees
• rotation (spinning, swinging, twisting etc.)

Question 3

Define relative angle.

Answer 3

• the angle formed between two adjacent body segments

- anatomical reference postion: relative angles are zero

Question 4

Define absolute angle.

Answer 4

angular orientation of a single body segment with respect to a fixed line of reference (vertical and horizontal reference)

Question 5

Define angular distance.

Answer 5

sum of angular changes undergone by rotating body

Question 6

Define angular displacement.

Answer 6

• assessed as difference of initial and final positions
• counter-clockwise (+) or clockwise (-)
• right hand rule

Question 7

What is the right hand rule?

Answer 7

• point the thumb of your right hand towards the positive linear direction along the axis of rotation
• the direction in which your fingers curl is the positive direction of rotation

Question 8

What are the 3 ways to measure angular distance?

Answer 8

• revolutions
• degrees
• radians

Question 9

1 rev = ______ degrees = ___ radians

Answer 9

360 degrees = 2π

Question 10

What is a degree?

Answer 10

1/360th of a revolution

Question 11

When L=r in calculating radians, this means what?

Answer 11

1 radian

Question 12

What is a radian?

Answer 12

the angle which includes the arc of a circle equal to the radius of the same circle

Question 13

1 radian = ___ degrees

Answer 13

57.3 degrees

Question 14

How do you convert from degrees to radians?

Answer 14

• multiply by π/180

- divide by 57.3

Question 15

How do you convert from radians to degrees?

Answer 15

• multiply by 180/π

- multiply by 57.3

Question 16

How do we measure angular displacement?

Answer 16

• by calculating the number of radians

Question 17

Describe the relationship between linear and angular displacement.

Answer 17

• the greater the distance of a given point on a rotating body from the axis of rotation, the greater the linear displacement of that point
• L = rθ

Question 18

How do the formulas for linear velocity and angular velocity differ?

Answer 18

• linear: v = d/t

- angular: ω = θ/t

Question 19

Describe the formula for angular speed and how it differs from the formula for angular velocity.

Answer 19

• angular speed = angular distance/change in time

- angular velocity = angular displacement/change in time

Question 20

What are the units for angular speed?

Answer 20

deg/s, rad/s, rpm

Question 21

Describe the relationship between linear and angular velocity.

Answer 21

• an object travelling in a circular path will follow a path that is a straight line when released (spiderman)
• the new path will be at a tangent to the radius of rotation (trebuchet)

Question 22

What is tangential velocity (v T)?

Answer 22

the velocity of the released object that was travelling in a circular path becomes linear velocity and changes from ω to v

Question 23

Describe the relationship between ω and v. Give examples.

Answer 23

• longer radius = greater linear velocity
• if all things are equal (angular velocities remain constant)
• ex. longer levers increase velocity (given equivalent ω)
• ex. baseball batter extends his arms before contact

Question 24

What is tangential acceleration?

Answer 24

the component of linear acceleration tangent to the circular path of a point on a rotating object

Question 25

In an object with constant ω, is there still acceleration?

Answer 25

yes. Linear acceleration: speeds up, slows down, or changes direction

Question 26

Describe linear acceleration that occurs in an object with constant ω.

Answer 26

• towards the centre
• centripetal (radial acceleration)
• force that causes this is centripetal force
• equal/opposite force = centrifugal force

Question 27

The _____ the distance of a given point on a rotating body from the axis of rotation, the
_____ the linear displacement of that point (assuming the same angular displacement)

Answer 27

greater, greater

Question 28

What is a tangent?

Answer 28

• line that just touches the arc created by a point on a rotating body
• perpendicular to the radius of the arc at that point

Question 29

longer vs shorter radius, ω equal for both, _____ radius will have greater vT

Answer 29

longer

Question 30

longer vs shorter radius, vT equal for both, _____ radius will have greater ω

Answer 30

shorter