Vector Operations and Angular Motion

These flashcards cover concepts related to vector operations, angular motion, and circular motion principles.

What is the result of vector addition A + B in terms of components i, j, and k?

A + B = (+)i + (-)j + (+-)k.

What does the dot product of two vectors A and B indicate?

The dot product A • B produces a scalar result.

What are the results of the cross product of vectors A and B?

The cross product A x B produces a vector.

What is the formula for scalar multiplication of a vector A = ai + bj + ck?

A = k(ai + bj + ck) where k is a scalar.

What does angular displacement represent?

Angular displacement is represented in radians [rad].

How is angular velocity represented?

Angular velocity is represented as ω in radians per second [rad/s].

What is the relationship between linear velocity and angular velocity?

Linear velocity v = ωr, where ω is the angular velocity and r is the radius.

What is the conversion from 1 revolution to radians?

1 revolution = 2π radians.

How can you convert RPM to radians per second?

1 RPM = 2π/60 rad/s.

What is angular acceleration (α) and how is it calculated?

Angular acceleration is α = Δω/Δt.

What is the equation relating initial angular velocity (ω₁) to angular acceleration (α)?

ω = ω₁ + αt.

What is the equation for the uniform circular motion relating to centripetal acceleration (aᶜ)?

Centripetal acceleration aᶜ = v²/r.

What does the centripetal force (Fᶜ) equation say?

Centripetal force Fᶜ = m(v²/r) where m is mass.

What happens to acceleration in a state of equilibrium in a system?

In equilibrium, the resultant acceleration is zero.

What is an important factor when converting linear to angular motion?

Always have the radius r when converting between linear and angular motion.

What does the formula v = wr imply about linear and angular velocity?

It shows the relationship where linear velocity is tangent to the circular path defined by angular velocity.

How do we calculate angular acceleration when considering two velocities?

Using α = (ω₂ - ω₁) / Δt.

What key aspect does the Centrifugal Force involve according to the notes?

Centrifugal Force is considered a 'fake' force due to inertia.

In the case of canonical pendulum, what is the force balance in vertical motion?

ΣF_y = 0, meaning Ty - W = 0.

What is the equation representing the balance of forces on a pendulum?

Tx - Fc = 0, where Tx is tension and Fc is centrifugal force.

How does an increase in angular velocity affect centripetal acceleration?

Centripetal acceleration increases as the square of angular velocity increases.

What role does the angle play in angular displacement?

Angle advanced over a specific time dictates the angular displacement.

What is the conversion factor for linear speed from km/h to m/s?

1000 km/h = (1000/3600) m/s.

What is the significance of the order of factors in vector cross products?

The order affects the direction and magnitude of the resulting vector.

What formula represents the relationship of centripetal acceleration to speed and radius?

aᶜ = v²/r.

What is the angular displacement in one complete revolution?

Angular displacement for one revolution is 2π radians.

What does it mean when it is stated that the diagonal order does alter the product in operations?

It highlights that the arrangement of the vectors being multiplied (e.g., in cross product) matters.

How is angular displacement calculated in reference to time?

Angular displacement is the angle advanced over a specific time.