Free Printable Rotation

1.

What is the unit for angular displacement?

a)

radians

b)

$\frac{rad}{s}$

c)

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

d)

degrees

2.

What is the unit for angular velocity?

a)

rad

b)

$\frac{rad}{s}$

c)

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

d)

$\frac{m}{s^2}$

3.

What is the unit for angular acceleration

a)

radians

b)

$\frac{rad}{s}$

c)

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

d)

degrees

4.

What is measured in radians per second?

a)

angular displacement

b)

angular acceleration

c)

angular velocity

d)

rpm

5.

What is measured in radians per second squared, (rad s^-2)?

a)

angular displacement

b)

angular acceleration

c)

angular velocity

d)

angular features

6.

the tendency of an object to resist a change in its motion

a)

acceleration

b)

inertia

c)

mass

7.

Objects with greater _________ also have greater inertia.

a)

speed

b)

mass

c)

friction

8.

A rod rotates about a pivot at its center at 2 rads/s. Its angular velocity increases to 14 rads/s in 3 s. Find the rod's angular acceleration

a)

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

b)

4 $\frac{rad}{s^2}$

c)

6 $\frac{rad}{s^2}$

d)

8 $\frac{rad}{s^2}$

9.

A record on a turntable is spinning and is coming to rest. If the angular velocity is 20.0 rad/s and the record slows at a rate of - 5 $\frac{rad}{s^2}$ , how long does it take the record to come to rest?

a)

2 s

b)

4 s

c)

12 s

d)

8 s

10.

A ball attached to a string and rotates in a circle. If it takes 1.00 s to complete one revolution, what is the angular velocity of the ball?

a)

3.14 rad/s

b)

6.28 rad/s

c)

9.42 rad/s

d)

12.6 rad/s

11.

A CD is rotating clockwise about its center as shown. At the instant shown, the CD has increasing angular velocity. Point Q is on the rim of the CD and point P is one half radius from the disc’s center. Which of the statements below is true?

a)

In one rotation, both points have the same angular displacement.

b)

In one rotation, both points travel the same distance.

c)

Point P is traveling faster than point Q.

d)

Both have points have the same centripetal acceleration.

12.

If the translational velocity of an object is 3 m/s, and is located a distance of 2 m from the axis of rotation, what is the object's angular velocity?

a)

0.67 rad/s

b)

1.5 rad/s

c)

5 rad/s

d)

6 rad/s

13.

An object completes 1.5 circular orbits in half a minute. What is its approximate angular velocity?

a)

0.05 rad/s

b)

0.30 rad/s

c)

0.5 rad/s

d)

3 rad/s

14.

An object completes 1.5 circular orbits in half a minute. It orbits with a radius of 2 m. What is the object's tangential speed?

a)

0.15 m/s

b)

0.60 m/s

c)

1.6 m/s

d)

6 m/s

15.

________________________ defined as the number of revolutions (cycles/rotations) completed in one second.

a)

Period

b)

Frequency

c)

Distance

d)

Centripetal acceleration

16.

Find the angular velocity of Earth

a)

7.3 x 10^-5 rad/s

b)

4.4 x 10^-3 rad/s

c)

3.7 x 10^-5 rad/s

d)

1.74 x10^-3

17.

The Moon rotates once on its axis in 27.3 days. Its radius is 1.74×10⁶ m.

. What is the period of the Moon’s rotation in seconds?

a)

2358720

b)

39312

c)

655.2

d)

10.92

18.

A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s. What is the wheel's average angular acceleration?

a)

9.6 rad/s/s

b)

4.8 rad/s/s

c)

3.1 rad/s/s

d)

1.6 rad/s/s

19.

A fan spins with a constant angular speed of 500 radians/second. How long will it take to cover an angle of 2π radians (one revolution)?

a)

0.013 s

b)

0.02 s

c)

785 s

d)

6.28 s

20.

A gear spins at a rate of 400 revolutions/minute. Which choice is closest to its angular speed in radians/second?

a)

6.67 rad/s

b)

2500 rad/s

c)

41.9 rad/s

d)

20.9 rad/s

21.

What is the Unit for Torque

a)

Nm

b)

N

c)

W

d)

J

22.

What is the weight of the package?

a)

5 N

b)

10 N

c)

15 N

d)

20 N

23.

What is the weight of the package?

a)

5 N

b)

10 N

c)

15 N

d)

20 N

24.

The derivative of a function is its

a)

Slope

b)

Maximum/Minimum

c)

Instantaneous rate of change

d)

Common Denominator

25.

What are the units of Force?

a)

kg m/s

b)

J

c)

N

d)

W

26.

What is the moment of inertia for the rod about an axis perpendicular to the rod and passing through point P, which is halfway between the center and the end of the rod? For a rod about its center:

$I=\frac{1}{12}mL^2$

a)

$\frac{1}{3}mL^2$

b)

$\frac{1}{48}mL^2$

c)

$\frac{7}{48}mL^2$

d)

$\frac{1}{6}mL^2$

27.

A woman sits on a spinning stool with her arms folded. When she extends her arms, which of the following occurs?

a)

She increases her moment of inertia, thereby increasing her angular speed.

b)

She increases her moment of inertia, thereby decreasing her angular speed.

c)

She decreases her moment of inertia, thereby increasing her angular speed.

d)

She decreases her moment of inertia, thereby decreasing her angular speed.

28.

Two identical cylindrical discs have a common axis. Initially one of the discs is spinning. When the two discs are brought into contact, they stick together. Which of the following is true?

a)

The total kinetic energy and the total angular momentum are unchanged from their initial values.

b)

Both the total kinetic energy and the total angular momentum are reduced by half.

c)

The total angular momentum is unchanged, but the kinetic energy of the spinning disk is reduced by half

d)

The total angular momentum is reduced by half, but the total kinetic energy is unchanged.

29.

A projectile of mass 0.2 kg and an initial velocity of 50 m/s

collides with the end of a blade attached to a turbine. The rotational inertia of the turbine is 12.5 . If the final rebound velocity of the projectile after hitting a turbine blade is −25 m/s, which of the following is most nearly the rotational velocity of the turbine after the collision?

a)

3.2 rad/s

b)

5.5 rad/s

c)

10.0 rad/s

d)

15.0 rad/s

30.

A rigid bar with a mass M and length L is free to rotate about a frictionless hinge at a wall. The bar has a moment of inertia I = $\frac{1}{3}ML^2$ about the hinge, and is released from rest when it is in a horizontal position as shown. What is the instantaneous angular acceleration when the bar has swung down so that it makes an angle of 30° to the vertical?

a)

$\frac{g}{3L}$

b)

$\frac{2g}{3L}$

c)

$\frac{3g}{4L}$

d)

$\frac{3g}{2L}$

31.

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

a)

A

b)

B

c)

C

d)

D

32.

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will reach the bottom first?

a)

cylinder

b)

pipe

c)

sphere

d)

They all reach the bottom at the same time.

33.

Which has greater angular speed, a horse near the outside rail of a merry-go-round or a horse near the inside rail?

a)

The inside horse

b)

The outside horse

c)

Neither - they both have the same angular speed

34.

In order to do a lot of flips an Olympic diver would want:

a)

A high rotational inertia

b)

A low rotational inertia

c)

A low linear acceleration

d)

A low angular velocity

35.

An object completes 1.5 circular orbits in half a minute. What is its approximate angular velocity?

a)

0.05 rad/s

b)

0.30 rad/s

c)

0.5 rad/s

d)

3 rad/s

36.

An object completes 1.5 circular orbits in half a minute. It orbits with a radius of 2 m. What is the object's tangential speed?

a)

0.15 m/s

b)

0.60 m/s

c)

1.6 m/s

d)

6 m/s

37.

Which of the following is NOT a unit of rotational speed?

a)

Meters per second

b)

Revolutions per minute

c)

Revolutions per second

d)

Rotations per second

38.

A bug on a turning phonograph record will make more turns per minute if it is located toward the center of the record.

a)

True

b)

False

39.

According to the Law of Conservation of Angular Momentum, if I (momentum of inertia) increases, what will happen to ω?

a)

Decrease

b)

Stay the same

c)

Increase

40.

The rotational equivalent to d (distance), v (velocity) and a (acceleration) are?

a)

m, m/s, m/s²

b)

θ, ω, α

c)

x, x/t, alphaα

d)

μ, Σ, τ

41.

A solid metal bar is at rest on a horizontal frictionless surface. It is free to rotate about a vertical axis at the left end. The figures show forces of different magnitudes that are exerted on the bar at different locations. In which case does the bar's angular speed about the axis increase at the fastest rate?

a)

A

b)

B

c)

C

d)

D

42.

In the diagram above, two masses, one with mass m, the other with mass M = 2m are resting on a uniform plank of length L that pivots at its midpoint. If the mass m is at the far end of the plank, how far away from the pivot should the mass M be to balance the plank in a horizontal position shown?

a)

L/2

b)

L/3

c)

L/4

d)

L/6

43.

A cylinder (I=¹/₂mr²) and a hoop (I=mr²) of the same radius and same mass are traveling at the same angular velocity (ω). What is the ratio of the rotational kinetic energy of the cylinder to the rotational kinetic energy of the hoop?

a)

1:1

b)

1:2

c)

2:1

d)

1:4

44.

A cylinder (I=¹/₂mr²) and a hoop (I=mr²) of the same radius and same mass are traveling at the same angular velocity (ω). What is the ratio of the angular momentum of the cylinder to the angular momentum of the hoop?

a)

1:1

b)

1:2

c)

2:1

d)

1:4

45.

A disk rotates with an angular speed $\omega$ . What is the linear speed v of a point on the disk located a distance r away from the axis of rotation?

a)

$\omega r$

b)

$\frac{\omega}{r}$

c)

$\frac{r}{\omega}$

d)

$\omega^2r$

46.

Suppose a bicycle wheel of radius R rolls without slipping for a linear distance x. What is the angular displacement the bicycle wheel during this movement?

a)

$\theta=\frac{x}{r}$

b)

$\theta=\frac{r}{x}$

c)

$\theta=xr$

d)

$\theta=xr^2$

47.

What does the slope of a $\omega$ vs t graph represent?

a)

The angular acceleration ( $\alpha$ )

b)

The angular velocity ( $\omega$ )

c)

The angular displacement ( $\Delta\theta$ )

d)

The torque ( $\tau$ )

48.

What does the slope of a $\theta$ vs t graph represent?

a)

The angular acceleration ( $\alpha$ )

b)

The angular velocity ( $\omega$ )

c)

The angular displacement ( $\Delta\theta$ )

d)

The torque ( $\tau$ )

49.

What does the area of a $\omega$ vs t graph represent?

a)

The angular acceleration ( $\alpha$ )

b)

The angular velocity ( $\omega$ )

c)

The angular displacement ( $\Delta\theta$ )

d)

The torque ( $\tau$ )

50.

What does the area of a $\alpha$ vs t graph represent?

a)

The angular acceleration ( $\alpha$ )

b)

The change in angular velocity ( $\Delta\omega$ )

c)

The angular displacement ( $\Delta\theta$ )

d)

The torque ( $\tau$ )

51.

If $\theta\left(t\right)=-16t^2+100$ , find the angular velocity of the object when t=1.

a)

-16 rad/s

b)

-48 rad/s

c)

-32 rad/s

d)

48 rad/s

52.

If $\theta=-16t^2+16t+32$ . What is the angular velocity at t=2?

a)

-48 m/s

b)

-32 m/s

c)

48 m/s

d)

-16 m/s

53.

If $\theta=t^2+1$ for a rotating object with a radius of 0.5m, what is the instantaneous linear velocity at t = 3s?

a)

6 m/s

b)

3 rad/s

c)

12 rad/s

d)

6 rad/s

54.

The angular velocity of a rotating object with a radius of 0.25m is given as $\omega\left(t\right)\ =\ 2t+3t^3$ . What is the angular acceleration of the object at t = 2 s?

a)

27 rad/s²

b)

38 rad/s²

c)

16 rad/s²

d)

49 rad/s²

55.

The angular velocity of a rotating object with a radius of 0.25m is given as $\omega\left(t\right)\ =\ 2t+3t^3$ . What is the linear acceleration of the object at t = 2 s?

a)

27 m/s²

b)

38 m/s²

c)

9.5 m/s²

d)

152 m/s²

Rotation

Total questions: 55

Worksheet time: 1hrs 16mins

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