Free Printable Rotational Kinematics

Worksheets

Rotational Kinematics

Total questions: 42

Worksheet time: 11hrs 30mins

Name

Class

Date

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

The inside horse

The outside horse

Neither - they both have the same angular speed

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)?

0.013 s

0.002 s

76.9 s

6.28 s

A merry go round starts from rest, and reaches an angular speed of 2 radians/second in 3 seconds. What is its angular acceleration, and through what angle does it sweep in the 3 second time interval?

α = 3/2 rad/s², θ=27/4 rad

α = 2/3 rad/s², θ=3 rad

α = 2/3 rad/s², θ=6 rad

α = 6 rad/s², θ=27 rad

A flywheel starts from rest, and has an angular acceleration of 4 rad/s². What will be its angular speed when it has made one revolution?

5.01 rad/s

50.27 rad/s

2.83 rad/s

7.09 rad/s

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

6.67 rad/s

2500 rad/s

41.9 rad/s

20.9 rad/s

Two bugs ride a turntable which is rotating at a constant rate of 4 rad/s. Bug A is at a radius of 4 cm, while bug B is at a radius of 8 cm. What is the velocity of bug B?

4 cm/s

32 cm/s

2 cm/s

1 cm/s

Two bugs ride a turntable which is rotating at a constant rate of 4 rad/s. Bug A is at a radius of 4 cm, while bug B is at a radius of 8 cm. Which of the following is true?

Bug A has a greater rotational speed.

Bug B has a greater rotational speed.

Bug A has a greater speed.

Bug B has a greater speed.

2600 rev/min is equivalent to which of the following?

2600 rad/s

43.3 rad/s

273 rad/s

60 rad/s

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?

9.6 rad/s²

1.6 rad/s²

4.3 rad/s²

6.2 rad/s²

10.

How do you find the tangential speed of a rotating circle?

v = ωr

v = ωr²

v = ωπ

v = ωπr

11.

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

Meters per second

Revolutions per minute

Revolutions per second

Rotations per second

12.

The angle through which a point, line, or body is rotated in a specific direction and around a specific axis •

angular velocity

angular displacement

radian

degree

13.

A flywheel starts from rest, and has an angular acceleration of 4 rad/s². What will be its angular speed when it has made 2 revolutions?

7.09 rad/s

6.35 rad/s

10.03 rad/s

5.01 rad/s

14.

A disk initially rotating at 125 rad/s is slowed down with a constant angular acceleration of magnitude 4.00 rad/s².

a. What is the original linear speed of a point on the disk that is 0.450 m from the axis?

18.9 m/s

22.1 m/s

56.25 m/s

48.3 m/s

15.

A mass is hung from a string that is wrapped around a wheel of known radius R on a rotational apparatus. The system is released from rest, and the mass accelerates towards the ground. A physics student measures the distance the mass falls as well as the time, and they calculate the acceleration of the mass as a.

What equation would allow the student to determine the angular acceleration of the apparatus as the mass falls with the given information?

$a=\alpha R$

$\omega=\omega_0+\alpha t$

$\alpha=\frac{\sum_{ }^{ }\tau}{I}$

$\omega^2=\omega_0^2+2\alpha\Delta\theta$

16.

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?

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

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

$\theta=xr$

$\theta=xr^2$

17.

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

The angular acceleration ( $\alpha$ )

The angular velocity ( $\omega$ )

The angular displacement ( $\Delta\theta$ )

The torque ( $\tau$ )

18.

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

The angular acceleration ( $\alpha$ )

The angular velocity ( $\omega$ )

The angular displacement ( $\Delta\theta$ )

The torque ( $\tau$ )

19.

- 8 rad/s²

+ 8 rad/s²

-100 rad/s²

-20 rad/s²

20.

- 100 rad

-100π rad

-40π rad

-200π radians

21.

Clockwise and speeding up

Counterclockwise and speeding up

Clockwise and Slowing down

Counterclockwise and slowing down

22.

You are making a circular turn in your car on a horizontal road when you hit a big patch of ice, causing the force of friction between the tires and the road to become zero. While the car is on the ice, it

continues to follow a circular path, but with a radius larger than the original radius.

moves along a straight-line path toward the center of the circle.

moves along a straight-line path away from the center of the circle

moves along a straight-line path in its original direction.

23.

Rotational Motion is motion ____________________________.

in a straight line

in the opposite direction

around a fixed point in space

that never stops.

24.

A disk initially rotating counterclockwise (CCW) at a certain constant angular speed is suddenly being pulled on by two strings T₁ and T₂, where T₂ > T_1.What is going to happen next?

The disk will continued rotating CCW at the constant angular speed.

The disk will continued rotating CCW but it will speed up

The disk will slow down and start rotating CW

The disk will eventually stop rotating

25.

How do you find the tangential speed of a rotating circle?

v = ωr

v = ωr²

v = ωπ

v = ωπr

26.

[5 points] An airliner arrives at the terminal and the engines are shut off. The rotor of one of the engines has an initial clockwise angular speed of 2000 rad/s. The engines rotation slows with an angular acceleration of magnitude 80 rad/s². Determine the angular speed after 10 s.

1200 rad/s

1225 rad/s

1000 rad/s

500 rad/s

27.

What does the term "tangential" mean?

Moving forward

Moving in a circle

Moving in a straight line

Moving around

28.

In uniform circular motion, there is a

Constant velocity

Constant angular velocity

Zero acceleration

Net tangential acceleration

29.

If the centripetal force on a particle in uniform circular motion is increased,

The tangential speed remains constant

The tangential speed will decrease

The radius of the circular path will increase

The tangential speed will increase and/or the radius will decrease

30.

The angular acceleration in circular motion

Is equal in magnitude to the tangential acceleration divided by the radius

Increases the angular velocity in the same direction

Has units of rad/s²

All of the above

31.

The SI units for ω are

rad

rad/s

rad/s²

seconds

32.

The SI units for Θ are

rad

rad/s

rad/s²

seconds

33.

The SI units for α are

rad

rad/s

rad/s²

seconds

34.

A tire of 68cm in diameter travels 9.2km. How many revolutions does it make?

43.00 rads

567 revs

4300 revs

68cm

35.

An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle q in the time t, through what angle did it rotate in the time 1/2 t?

$\frac{1}{2}\theta$

$\frac{1}{4\ }\theta$

$\frac{3}{4\ }\theta$

$2\ \theta$

36.

What is the angular speed in rad/s of the minute hand of a clock?

Impossible to solve from the given information.

1.05 rad/s

0.105 rad/s

0.00105 rad/s

37.

A 10-m plank is being moved by rolling it over two cylindrical logs placed 2 m from either end of the plank. As the plank is pushed, the logs roll on the ground without slipping, and they do not slip with respect to the plank. How far can the plank be moved before the rear log reaches the end of the plank?

8 m

2 m

3 m

4 m

38.

Earth's radius is 6.38 × 10⁶ m, and it completes one revolution every day. What is the tangential speed of a person standing on the equator?

232 m/s

148 m/s

464 m/s

21.5 m/s

39.

A child is riding a merry-go-round, which has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s². The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the acceleration of the child?

8.05 m/s²

7.27 m/s²

2.58 m/s²

3.46 m/s²

40.

Two wheels with fixed centers are in contact with each other and rotate without slipping. Wheel A has a radius of 12.0 cm and is rotating with an angular speed of 35.0 rad/s. Wheel B has a radius of 17.0 cm. What is the angular speed of wheel B?

49.6 rad/s

24.7 rad/s

5.83 rad/s

4.97 rad/s

41.

A bowling ball with a radius of 12 cm is given a backspin (i.e. if the ball is moving to the right it is spinning counterclockwise at the same time) of 8.3 rad/s and a forward velocity of 8.5 m/s. As a result, the ball slides along the floor. What is the forward velocity of the point on the ball that is touching the floor?

7.5 m/s

9.5 m/s

11.5 m/s

13.5 m/s

42.

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger linear displacement?

Child A

Child B

They have the same zero linear displacement.

They have the same non-zero linear displacement.

100 %

Rotational Kinematics

Total questions: 42

Worksheet time: 11hrs 30mins

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