Engineers test a prototype motor by recording its angular acceleration over the first…

MATHEMATICS · Multi-part · A Level · Mathematics · Quantities and units in mechanics · Quantities and units in mechanics

Problem

Engineers test a prototype motor by recording its angular acceleration over the first

5.0\,\text{s}

of operation. The data, shown below, describe how

\alpha

varies with time: • From

t=0

t=2.0\,\text{s}

\alpha

increases uniformly from

0

4.0\,\text{rad/s}^2

. • From

t=2.0\,\text{s}

t=5.0\,\text{s}

\alpha

remains constant at

4.0\,\text{rad/s}^2

. A painted dot is located on the surface of the motor’s cylindrical drum at a radius of

0.40\,\text{m}

from the axis. Ignore any other forces on the drum. (a) On your answer sheet, sketch a graph of the dot’s tangential acceleration

a_{t}

versus time for the interval

0 \le t \le 5.0\,\text{s}

. Clearly label the key numerical values on both axes. (b) Determine the value of the dot’s tangential acceleration at

t = 3.5\,\text{s}

. (c) Calculate the average tangential acceleration of the dot over the entire

5.0\,\text{s}

interval. Show how you obtain your result.