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 6 6 6 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/s2. 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/s2. 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 5 4 0
  • B 5 , 4 0 0
  • C 2 , 7 0 0
  • D 2 7 0
  • E 2 2 5

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 1 5 5 .

Q13:

An angular displacement of 0.45 rad is equal to revolutions.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.