Rotational Position & Displacement

While you drive, your tires, all of radius 0.40 m, rotate 10,000 times. How far did you drive, in meters?

An object moves a total distance of 1,000 m around a circle of radius 30 m. How many degrees does the object go through? 

BONUS:How many complete revolutions does it make?

A car travels a total of 2,000 m and 1140° around a circular path, starting from 0° . What is the radius of the circular path? 

BONUS:How far (in degrees) from 0° does the car end up?

Calculate the rotational velocity (in rad/s) of a clock’s minute hand. 

EXTRA:Calculate the rotational velocity (in rad/s) of a clock’s hour hand.

A wheel of radius 5 m accelerates from 60 RPM to 180 RPM in 2 s. Calculate its angular acceleration.

A tiny object spins with 5 rad/s around a circular path of radius 10 m. The object then accelerates at 3 rad/s². Calculate its angular speed 8 s after starting to accelerate.

BONUS:Calculate its linear displacement in the 8 s.

The turntable of a DJ set is spinning at a constant rate just before it is turned off. If the turntable decelerates at 3 rad/s² and goes through an additional 30 rotations before stopping, how fast (in RPM) was the turntable initially spinning? 

BONUS:How long (in seconds) does the turntable take to stop?

A disc of radius 10 m rotates around itself with a constant 180 RPM. Calculate the linear speed at a point 7 m from the center of the disc.

A rock rotates around a light, 4-m long string. The rock is initially at rest, but reaches 150 RPM in 3 seconds. Calculate its tangential acceleration after 3 s. 

BONUS:Calculate its tangential speed after 3 s.

A 4 m long blade initially at rest begins to spin with 3 rad/s² around its axis, which is located at the middle of the blade. It accelerates for 10 s. Find the tangential speed of a point at the tip of the blade 10 s after it starts rotating.

A large disc of radius 10 m initially at rest takes 200 full revolutions to reach 30 RPM. Calculate the total linear acceleration of a point at half way between the disc’s center and its edge, once the disc reaches 30 RPM. (You may assume it continues accelerating past that point)

An object of negligible size moves in a circular path of radius 20 m with 90 RPM. Find its radial acceleration.

A long, light rope is wrapped around a cylinder of radius 40 cm, which is at rest on a flat surface, free to move. You pull horizontally on the rope, so it unwinds at the top of the cylinder, causing it to begin to roll without slipping. You keep pulling until the cylinder reaches 10 RPM. Calculate the speed of the rope at the instant the cylinder reaches 10 RPM.