A solid wheel spins about a fixed axle through its center

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

Problem

A solid wheel spins about a fixed axle through its center. The angular velocity of the wheel varies with time as described below: • At

t = 0\,\text{s}

\omega = 0\,\text{rad/s}

. • Between

t = 0\,\text{s}

and

t = 3\,\text{s}

\omega

increases uniformly to

6\,\text{rad/s}

. • From

t = 3\,\text{s}

t = 5\,\text{s}

\omega

remains constant at

6\,\text{rad/s}

. A small block of clay is firmly attached to the rim of the wheel at a radius of

0.24\,\text{m}

. (a) Calculate the magnitude of the clay’s tangential acceleration at

t = 1.5\,\text{s}

. (b) Determine the clay’s linear speed at

t = 4.0\,\text{s}

. (c) Compute the total linear distance traveled by the clay from

t = 0\,\text{s}

t = 5\,\text{s}

. (d) At

t = 5\,\text{s}

, the wheel is suddenly brought to rest in

0.50\,\text{s}

by a uniform angular deceleration. Determine the magnitude of the clay’s average tangential acceleration during this stopping interval.