Connections Between Linear and Rotational Quantities

These flashcards cover key concepts related to linear and rotational motion, including equations of motion, energy, torque, and angular momentum.

What is the equation that relates arc length to radius and angular displacement?

s = r ∆θ

How is the linear velocity of a rolling object related to its radius and angular velocity?

vt = r ω

What is the formula for tangential acceleration in terms of radius and angular acceleration?

at = r α

What is the general expression for rotational kinetic energy?

K = Ktranslation + Krot

What is the relation between torque and force?

Torque (τ) = r × F

What is the formula that defines the moment of inertia in rotational motion?

I = ∑ m r² for discrete masses.

What is the equation for total kinetic energy of a rolling object?

K = ½ m v² + ½ I ω²

In a rolling without slipping condition, how is linear speed expressed in terms of translational speed?

vcm = vt.

What relates the net torque to angular acceleration?

Torque (τ) net = I α.

For a simple yo-yo falling, what conservation principle can be applied when analyzing its motion?

∆K + ∆U = W_n (Work-energy principle).

Which object, a disk or a hoop, will reach the bottom of an incline first?

A disk will reach the bottom before the hoop.