AP Physics 1: Algebra-Based 5.1 A Describe the Rotation of a System with Respect to Time Using Angular Displacement Angular Velocity and Angular Questions

Practise describing rotational motion with angular displacement, velocity and acceleration, including unit conversions and relationships among their time graphs.

Exam points

compare the angular speeds of different points fixed on the same rotating rigid system
calculate angular displacement in radians from the area under an angular velocity-time graph
convert rotational rates such as RPM to rad/s before finding average angular acceleration
sketch angular displacement-time graphs whose slopes match the given angular velocity
construct angular velocity-time and acceleration-time graphs for piecewise rotational motion

[Maximum number: 2]

(7 points, suggested time 13 minutes)

Two pulleys with different radii are attached to each other so that they rotate together about a horizontal axle through their common center. There is negligible friction in the axle. Object 1 hangs from a light string wrapped around the larger pulley, while object 2 hangs from another light string wrapped around the smaller pulley, as shown in the figure above.
$m_{0}$ is the mass of object 1.
$1.5 m_{0}$ is the mass of object 2.
$r_{0}$ is the radius of the smaller pulley.
$2 r_{0}$ is the radius of the larger pulley.

On the axes below, sketch a graph of the angular velocity $\omega$ of the system consisting of the two pulleys as a function of time t. Include the entire time interval shown. The pulleys are released at t=0, and the string is cut at $t=t_{C}$ .

For a linear graph between 0 and $t_{C}$ , with an initial angular velocity of zero and nonzero slope 1 point
Scoring note: The slope can be positive or negative.
For a change in the sign of the slope at $t=t_{C}$ 1 point
AND
no discontinuity.
Example response for part (c)

Figure for Answer to Question AP Physics 1: Algebra-Based 5.1 A Describe the Rotation of a System with Respect to Time Using Angular Displacement Angular Velocity and Angular Questions question 1 — AP Physics 1: Algebra-Based

Total for part (c)

for question 57 points

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AP Physics 1: Algebra-Based 5.1 A Describe the Rotation of a System with Respect to Time Using Angular Displacement Angular Velocity and Angular Questions question 1