Physics - Chapter 8

What is a rigid body?

Object whose shape and mass distribution do not change during motion

What are the three types of rigid body motion?

Translation, rotation, and combined motion

What defines rotational motion?

All points move in circles about the same axis

What is angular displacement (θ)

Rotation angle defined by arc length divided by radius

What is the formula for angular displacement?

θ = l / r

What is a radian?

Angle where arc length equals radius

Why is θ dimensionless?

Is it a ratio of two lengths

What must θ be measured in for formulas to work?

Radians

What is angular velocity?

Rate of change of angular displacement

What is the formula for angular velocity?

ω = Δθ / Δt

What is angular acceleration (α)?

Rate of change of angular velocity

What is the formula for angular acceleration?

α = Δω / Δt

What quantities are the same for all points in a rigid body?

Angular velocity and angular acceleration

What is the linear velocity formula in rotation?

v = rω

What does linear velocity depend on?

Distance from axis (r)

What is tangential acceleration?

Linear acceleration along motion direction

What is the tangential acceleration formula

a_t = rα

What is radial (centripetal) acceleration?

Acceleration toward center in circular motion

What is the centripetal acceleration formula?

a_r = rω²

Does centripetal acceleration exist if speed is constant?

Yes

When does tangential acceleration exist?

When angular velocity is changing

What is total acceleration in rotation?

Vector sum of tangential and radial accelerations

What condition is required for rotational kinematics equations?

Constant angular acceleration

What unit condition is required for kinematics equations?

Angles must be in radians

What is the rotational version of Newton's 1st Law?

Rotation continues unless external torque acts

What is torque (τ)?

Force that causes rotation

What is the basic torque formula?

τ = r⊥F

What is the full torque formula with angle?

τ = rF sinθ

What is the lever arm (r⊥)?

perpendicular distance from axis to line of force

When is torque maximized?

When force is perpendicular (θ = 90°)

When is torque zero?

When force is parallel to radius

What is moment of inertia (I)?

Resistance to rotational motion

What determines moment of inertia?

Mass and its distance from axis

What is the formula for moment of inertia?

I = Σmr²

How does distance affect inertia?

Larger radius increases inertia

What is rotational Newton's 2nd Law?

Net torque equals Iα

What is the formula for rotational dynamics?

Στ = Iα

What is rotational kinetic energy?

Energy due to rotation

What is the rotational kinetic energy formula

KE = (1/2)Iω²

What two motions make up rolling motion?

translation and rotation

What is rolling without slipping condition?

v = rω

What is total kinetic energy in rolling?

KE = (1/2)mv² + (1/2)Iω²

What is the linear equivalent of θ?

x

What is the linear equivalent of ω?

v

What is the linear equivalent of α?

a

What is the rotational equivalent of force?

Torque

What is the rotational equivalent of mass?

Moment of inertia