A solid cylindrical disk of mass and radius is free to rotate about its central axle

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A solid cylindrical disk of mass

2.5\,\text{kg}

and radius

0.20\,\text{m}

is free to rotate about its central axle. A constant

1.6\,\text{N}\!\cdot\!\text{m}

torque acts on the disk for a time interval

t

. At

t=0

the disk’s angular velocity is

\omega_0 = 4.0\,\text{rad/s}

. (1) Derive an expression for the disk’s angular velocity

\omega(t)

as a function of time during the interval the torque is applied. (2) Using your result from part (a), determine the disk’s angular velocity after

3.0\,\text{s}

. (3) Starting from fundamental principles, obtain a rotational kinematic relation that is directly analogous to the translational equation

v^2 = v_0^2 + 2a\,\Delta x

. Show each step of your derivation. (4) Describe explicitly how each symbol in your rotational equation from part (c) corresponds to a symbol in the translational equation. Comment on any limitations of this one-to-one mapping.

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