# Worksheet: Rotational Kinematics

In this worksheet, we will practice modeling the change of the position with time of objects that move along circular paths.

**Q1: **

A car drives repeatedly around a roundabout. The car has a constant angular velocity of 1.4 rad/s. What is the period of the car’s circular motion?

- A 4.5 s
- B 0.22 s
- C 1.4 s
- D 2.2 s
- E 0.45 s

**Q2: **

A helicopter flies in a circle of radius 375 m, taking a time of 42 s to complete one revolution. What is the magnitude of the acceleration of the helicopter toward the center of its circular path?

**Q3: **

An angular displacement of is equal to an angular displacement of 7.25 rad.

- A78
- B127
- C831
- D208
- E415

**Q4: **

The wheels of a moving car rotate 13.5 times per second. What is the angular velocity of a point on the wheel that is not at the axis of the rotation of the wheel?

- A 85 rad/s
- B 12 rad/s
- C 0.012 rad/s
- D 42 rad/s
- E 0.085 rad/s

**Q5: **

A drill bit is initially at rest. When the drill is activated, the drill bit rotates 47.5 times per second. The drill bit reaches this speed in a time of 175 ms. What is the angular acceleration of the drill bit?

**Q6: **

An angular displacement of is equal to revolutions.

- A1.85
- B3.70
- C6.66
- D5.81
- E11.6

**Q7: **

The blades of a large wind turbine rotate fully in a time of
3.25 s when it is operating at its full speed. The angular acceleration of the
turbine while increasing to its full speed is 0.124 rad/s^{2}. How much
time is required to bring an initially inactive turbine to its full operating
speed?

**Q8: **

A felled tree trunk rolls down a slope in a time of 7.2 s. The trunk is initially at rest at the top of the slope and has an angular velocity of 12 rad/s at the base of the slope. How many times does the trunk completely rotate as it rolls down the slope?

**Q9: **

A wheel of a moving car comes to rest in a time of 8.4 s
when a brake pad is applied to it. The magnitude of the wheel’s initial angular velocity is 5.5 rad/s,
and its angular deceleration is 2.2 rad/s^{2}.
How many complete rotations did the wheel make before coming to rest?

- A17 rotations
- B11 rotations
- C19 rotations
- D12 rotations
- E14 rotations

**Q10: **

An ice-skater spins around her axis of rotation 2.5 times per second. Her arms are outstretched to different lengths while she spins. The skater’s fingertip on one arm is 1.3 m from the skater’s axis of rotation, and her fingertip on the other arm is 0.45 m from her axis of rotation. What is the difference between the angular velocity of the skater’s fingertips on one of her arms compared to her other arm?

**Q11: **

A satellite has a circular orbit around Earth with a period of 1.6 hours.

How many degrees is the angular displacement of the satellite during a single Earth day to the nearest degree?

- A
- B
- C
- D
- E

How many radians is the angular displacement of the satellite during a single Earth day to the nearest radian?

- A 94 rad
- B 47 rad
- C 9 rad
- D 2 rad
- E 5 rad

**Q12: **

An angular displacement of radians is equal to an angular displacement of .

**Q13: **

An angular displacement of 0.45 rad is equal to revolutions.