Worksheet: Rotational Kinematics
In this worksheet, we will practice modeling the change of the position with time of objects that move along circular paths.
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
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?
An angular displacement of is equal to an angular displacement of 7.25 rad.
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
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?
An angular displacement of is equal to revolutions.
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?
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?
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
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?
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?
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
An angular displacement of radians is equal to an angular displacement of .
An angular displacement of 0.45 rad is equal to revolutions.