Question

A cylinder in a machine is initially at rest. It then has an angular acceleration of3rad/s^2 for 18s.Determine the (a)angle through which the cylinder has spun, and (b) the cylinder's final angular speed.

Answer 1

Answer 2

(a) Angle Spun (θ):

The cylinder rotates through 486 radians.

Calculation:
Using the kinematic equation for rotational motion (since initial angular velocity ${\omega }_0=0$):

$$\theta =\frac{1}{2}\alpha t^2=\frac{1}{2}\times 3{\text{rad/s}}^2\times (18\text{s}{)}^2=486\text{rad}$$

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(b) Final Angular Speed (ω):

The cylinder’s final angular speed is 54 rad/s.

Calculation:
Using $\omega ={\omega }_0+\alpha t$:

$$\omega =0+3{\text{rad/s}}^2\times 18\text{s}=54\text{rad/s}$$

Summary:

• (a) Angle rotated: 486 radians

• (b) Final angular speed: 54 rad/s