Free Printable Rotational Kinematics (AP1)

1.

An object rotates with an angular speed that varies with time, as shown in the graph. How can the graph be used to determine the magnitude of the angular acceleration α of the object? Justify your selection.

a)

Subtract the greatest value of the angular speed from the smallest value of the angular speed, because α=Δω.

b)

Determine the slope of the line from 0s to 2s, because the slope represents Δω/Δt.

c)

Determine the area bounded by the line and the horizontal axis from 0s to 2s, because α = 1/2ωΔt.

d)

The angular acceleration cannot be determined without knowing the rotational inertia of the object.

2.

Which Which of the following graphs, if any, shows the angular velocity ω of the pulley as a function of time t after the block is released from rest?

a)

b)

c)

d)

3.

Using the graph above, determine the angular velocity $\omega$ of the system.

a)

10 rad/sec

b)

25 rad/sec

c)

50 rad/sec

d)

2 rad/sec

4.

The graph shows the angular velocity ωω as a function of time tt for a point on a rotating disk. The magnitude of the angular acceleration of the disk at t=2s is most nearly...

a)

0.7 $\frac{rad}{s^2}$

b)

1.5 $\frac{rad}{s^2}$

c)

10.0 $\frac{rad}{s^2}$

d)

20.0 $\frac{rad}{s^2}$

5.

The graph shows the angular velocity ω as a function of time t for a point on a rotating disk. How far does the disk rotate from 0 to 4 sec?

a)

32 rad

b)

20 rad

c)

8 rad

d)

1.5 rad

6.

Two identical wheels, wheel 1 and wheel 2, initially at rest begin to rotate with constant angular accelerations α. After rotating through the same angular displacement, $\Delta\theta_0$ , the angular velocity of wheel 1 is $\omega_1$ and the angular velocity of wheel 2 is $\omega_2=3\omega_1$ . How does the angular acceleration of wheel 2, $\alpha_2$ , compare to the angular acceleration of wheel 1, $\alpha_1$ ?

a)

$\alpha_2=\alpha_1$

b)

$\alpha_2=\frac{\alpha_1}{3}$

c)

$\alpha_2=3\alpha_1$

d)

$\alpha_2=9\alpha_1$

7.

A graph of the angular velocity ω as a function of time t is shown for an object that rotates about an axis. Three time intervals, 1–3, are shown. Which of the following correctly compares the angular displacement Δθ of the object during each time interval?

a)

$\Delta\theta_1=\Delta\theta_3>\Delta\theta_2$

b)

$\Delta\theta_2>\Delta\theta_1=\Delta\theta_3$

c)

$\Delta\theta_3>\Delta\theta_2>\Delta\theta_1$

d)

$\Delta\theta_1>\Delta\theta_2>\Delta\theta_3$

8.

An object revolves around a central axis of rotation. The motion of the object is described by the following equation.

$\omega^2=\left(10\ \frac{rad}{s}\right)^2-\left(4\ \frac{rad}{s^2}\right)\theta$

Which two of the following graphs correctly shows the angular motion of the object? Select two answers.

a)

b)

c)

d)

9.

A uniform disk spins about an axis that passes through the center of the disk and is perpendicular to the plane of the disk, as shown in Figure 1. The disk has an initial angular velocity of $\omega_d$ and uniformly accelerates to rest over time. The angular velocity of the disk as a function of time is shown in Figure 2. A student must determine the angular displacement of a point on the edge of the disk from t=0 to the instant in time the disk comes to rest if the point’s initial velocity is changed to $2\omega_d$ but its angular acceleration is the same as shown in Figure 2. How can the graph in Figure 2 be changed before the student can determine the angular displacement? Justify your selection.

a)

Recreate the graph with a vertical intercept that is twice the value of the intercept shown in Figure 2, because the angular velocity is increased from $\omega_d$ to $2\omega_d$ . The horizontal intercept should be the same in both graphs, because the angular acceleration is the same in both graphs.

b)

Recreate the graph with a vertical intercept that is twice the value of the intercept shown in Figure 2, because the angular velocity is increased from $\omega_d$ to $2\omega_d$ . The slope of the line should be the same in both graphs, because the angular acceleration is the same in both graphs.

c)

Recreate the graph with the same vertical intercept in both graphs, because the angular acceleration is the same in both graphs. The slope of the curve in the new graph should be twice as steep as the slope in Figure 2, because the angular velocity is increased from $\omega_d$ to $2\omega_d$ .

d)

Recreate the graph with the same vertical intercept in both graphs, because the angular acceleration is the same in both graphs. The horizontal intercept in the new graph should be twice the value of the horizontal intercept in Figure 2, because the angular velocity is increased from $\omega_d$ to $2\omega_d$ .

Rotational Kinematics (AP1)

Total questions: 9

Worksheet time: 18mins

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