Rotational Kinematics (College Board AP® Physics 1: Algebra-Based): Exam Questions

Define the term angular speed.

A fairground wheel rotates clockwise at a constant rate of $1.5\mathrm{rpm}$.

Determine the angular speed of the wheel in $\mathrm{rad}/\mathrm{s}$.

Figure 1

A passenger enters a car at the bottom of the fairground wheel, as shown in Figure 1. At time $t=0$, the wheel begins to rotate.

i) Calculate the angular displacement, in $\mathrm{rad}$, of the passenger at time $t=30\mathrm{s}$.

ii) Draw a circle around a car on the diagram in Figure 1 to show the angular position of the passenger at time $t=30\mathrm{s}$.

The passenger leaves the car after the fairground wheel has completed 6 revolutions.

Calculate how long the passenger spends on the fairground wheel.

Define the term angular acceleration.

A car with $0.45\mathrm{m}$ diameter tires is initially moving at a constant speed of $24\mathrm{m}/\mathrm{s}$.

Calculate the angular velocity of the tires, and state the direction.

The car decelerates uniformly from its initial speed of $24\mathrm{m}/\mathrm{s}$ to rest after the tires complete 42 revolutions.

i) Calculate the angular displacement of the tires.

ii) Calculate the angular acceleration of the tires, and state the direction.

Calculate the linear distance traveled by the car as it comes to rest.

State the conditions required for the rotational kinematic equations to be used.

A disk starts spinning from rest when it undergoes a constant angular acceleration. After $10\mathrm{s}$, the disk spins with angular speed $18\mathrm{rad}/\mathrm{s}$.

Calculate the angular acceleration of the disk.

The disk continues to accelerate until it has rotated through an angular displacement of $360\mathrm{rad}$.

Determine the final angular speed of the disk.

The disk has a radius of $20\mathrm{cm}$. Once the disk has reached its final angular speed, two coins are dropped from rest onto the disk. Coin 1 is dropped at a point $10\mathrm{cm}$ from the disk's center. Coin 2 is dropped at the edge of the disk.

Indicate whether the tangential speed of Coin 2 is greater than, equal to, or less than the tangential speed of Coin 1. Justify your answer.

Figure 1

The graph in Figure 1 shows the angular position of a vinyl record as a function of time. Take counterclockwise to be the positive direction.

i) Describe the motion of the vinyl record using information from the graph in Figure 1.

ii) Using data from the graph in Figure 1, calculate the angular velocity of the vinyl record at $t=4\mathrm{s}$.

Figure 2

The graph in Figure 2 shows the angular velocity of a different vinyl record as a function of time.

i) Describe the motion of the vinyl record using information from the graph in Figure 2.

ii) Using data from the graph in Figure 2, calculate the angular displacement of the vinyl record at $t=4\mathrm{s}$.

iii) Using data from the graph in Figure 2, calculate the angular acceleration of the vinyl record between $t=1\mathrm{s}$ and $t=3\mathrm{s}$.

On the axes in Figure 3, sketch and label two lines to represent the angular accelerations of the vinyl records in part b) and c) as functions of time. Each line should be distinctly labeled.

Figure 3