KIN 3514 Exam 2: Angular Kinematics

What is angular motion?

Motion around an axis of rotation.

Examples of angular motion?

Spinning, swinging, twisting, rotating.

What units are used to describe angular motion?

Degrees and radians.

How many degrees are in 1 radian?

About 57.3°.

What is a radian?

The angle where the arc length equals the radius.

What is the formula for radians?

θ = s / r

What does s represent?

Arc length.

What does r represent?

Radius.

When θ = 1 radian, what is true?

Arc length = radius.

Are radians unitless?

Yes, because length/length cancels out.

What is an absolute angle?

The angle between a body segment and a fixed reference line (usually horizontal).

How are absolute angles measured?

From a horizontal (or vertical) reference line at the distal end of the segment.

In what direction are absolute angles typically measured?

Counterclockwise.

Examples of segments measured with absolute angles?

Thigh, trunk, shank, foot.

What is a relative angle?

The angle between two adjacent body segments.

What is another name for relative angles?

Joint angles.

What is the reference for relative angles?

The longitudinal axes of two connected segments.

What is the typical "neutral" position for joint angles?

Fully extended (0° or sometimes 180°).

Does it matter if you use 0° or 180°?

No, as long as you are consistent.

Hip joint angle convention?

Positive → flexion

Negative → extension

Knee joint angle convention?

Positive → flexion

Negative → extension

Ankle joint angle convention?

Positive → dorsiflexion

Negative → plantarflexion

What rule is used to determine the direction of angular vectors?

The Right-Hand Thumb Rule.

What does the Right-Hand Thumb Rule describe?

The direction of angular momentum or torque.

How do you use the Right-Hand Thumb Rule?

Curl your fingers in the direction of rotation; your thumb points in the direction of the vector.

What do the curled fingers represent?

The direction of rotation.

What does the thumb represent?

The direction of the angular vector (torque or angular momentum).

What direction is considered positive rotation?

Counterclockwise.

What direction is considered negative rotation?

Clockwise.

What is angular displacement?

The change in angular position of a rotating object.

How is angular displacement calculated?

Final angle − initial angle.

Is angular displacement a scalar or vector?

Vector (has direction).

What units are used for angular displacement?

Degrees (°) or radians (rad).

What direction is positive angular displacement?

Counterclockwise.

What direction is negative angular displacement?

Clockwise.

What must be included when calculating angular displacement?

All full rotations plus any partial rotation.

Why shouldn't angular displacement be confused with linear displacement?

Angular displacement measures rotation, not distance traveled.

When is θ = s/r valid?

Only when θ is in radians.

If an object travels 185 m on a circular path with radius 9 m, what is θ?

θ = 185 / 9 = 20.56 rad

What happens if the object completes more than one full rotation?

You must include all rotations in the total angular displacement.

What is angular distance?

The total amount of rotation, found by summing the magnitudes of all angular changes.

Is angular distance a scalar or vector?

Scalar (no direction).

What units are used for angular distance?

Degrees (°) or radians (rad).

What is angular velocity?

The rate of change of angular displacement.

What is the formula for angular velocity?

ω = Δθ / Δt

Is angular velocity a scalar or vector?

Vector.

What units are used for angular velocity?

rad/s or deg/s.

What happens when angular displacement increases in the same time?

Angular velocity increases.

What is tangential velocity?

The linear velocity of an object moving along a circular path.

What is the formula for tangential velocity?

vₜ = rω or vₜ = (Δθ · r) / Δt

What direction is tangential velocity?

Tangent to the circular path and perpendicular to the radius.

What happens to tangential velocity as radius increases?

It increases (vₜ ∝ r).

Why does a point farther from the center move faster?

It travels a longer arc in the same time.

If angular velocity is the same for all points, what differs?

Tangential (linear) velocity.

Do all points on a rotating object have the same angular velocity?

Yes.

Do all points have the same tangential velocity?

No, it depends on radius.

What is angular acceleration?

The rate of change of angular velocity.

What is the formula for angular acceleration?

α = Δω / Δt

What is tangential acceleration?

The linear acceleration caused by angular acceleration.

What is the formula for tangential acceleration?

aₜ = rα

What does tangential acceleration affect?

The speed (magnitude) of velocity.

In what direction does tangential acceleration act?

Tangent to the circular path.

What is centripetal acceleration?

Acceleration directed toward the center of rotation. Keeps an object moving in a circular path.

What does centripetal acceleration change?

Direction of velocity (not speed).

Which acceleration changes speed?

Tangential acceleration (aₜ)

Which acceleration changes direction?

Centripetal acceleration (a_c)

Can an object move in a circle without acceleration?

No, centripetal acceleration is always required.

What happens without centripetal acceleration?

The object moves in a straight line.