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What is angular position?
The angle (in radians) through which a point or line has been rotated about a specified axis.
What is angular velocity?
The rate of change of angular position with respect to time, measured in radians per second (rad/s).
What is angular acceleration?
The rate of change of angular velocity with respect to time, measured in radians per second squared (rad/s²).
Define rotational motion.
Motion of an object around a fixed axis.
What does 'rolling without slipping' mean?
A condition where the point of contact of a rolling object with the surface is instantaneously at rest. There is a torque acting on the object allowing it to rotate and translate simultaneously.
What is the effect of applying a constant angular acceleration to an object initially at rest?
The object's angular velocity increases uniformly over time.
What is the effect of a non-zero net torque on an object?
It causes angular acceleration.
What is the effect of an object rolling without slipping?
There is a direct relationship between its linear and angular velocities (v = rω) and accelerations (a = rα).
What happens if a wheel rolls with slipping?
The relationship v = rω no longer holds true, as the linear velocity is not solely determined by the angular velocity and radius.
What is the effect of increasing the radius of a wheel, given a constant angular velocity?
The linear velocity of a point on the edge of the wheel increases (v = rω).
What is the difference between translational and rotational displacement?
Translational: Δx (change in position, meters) | Rotational: Δθ (change in angular position, radians)
What is the difference between translational and rotational velocity?
Translational: v (linear velocity, m/s) | Rotational: ω (angular velocity, rad/s)
What is the difference between translational and rotational acceleration?
Translational: a (linear acceleration, m/s²) | Rotational: α (angular acceleration, rad/s²)
Compare the formulas: v = v₀ + at and ω = ω₀ + αt
v = v₀ + at: Final linear velocity equals initial linear velocity plus linear acceleration times time. | ω = ω₀ + αt: Final angular velocity equals initial angular velocity plus angular acceleration times time.
Compare the formulas: x = x₀ + v₀t + 1/2at² and θ = θ₀ + ω₀t + 1/2αt²
x = x₀ + v₀t + 1/2at²: Final linear position equals initial linear position plus initial linear velocity times time plus one-half linear acceleration times time squared. | θ = θ₀ + ω₀t + 1/2αt²: Final angular position equals initial angular position plus initial angular velocity times time plus one-half angular acceleration times time squared.
Compare the formulas: v² = v₀² + 2a(x - x₀) and ω² = ω₀² + 2α(θ - θ₀)
v² = v₀² + 2a(x - x₀): Final linear velocity squared equals initial linear velocity squared plus two times linear acceleration times change in linear position. | ω² = ω₀² + 2α(θ - θ₀): Final angular velocity squared equals initial angular velocity squared plus two times angular acceleration times change in angular position.