### Objective

To become familiar on the rotational Kinematics Equations

Equipment.

Blank paper
Calculator (a calculator is located on the widget page)
Pen or pencil

Problem 1

The diameter of a tire is 64.8 cm. A tack is embedded in the tread of the right rear tire. What is the magnitude and direction of the tack's angular velocity vector if the vehicle is traveling at 10.0 km/h?

### Problem 2

A spot of paint on a tire moves in a circular path of radius 0.42 m. Through what angle must the tire rotate for the spot to travel 1.48 m?

### Problem 3

A propeller (arm length 1.2 m) starts from rest and begins to rotate counterclockwise with a constant angular acceleration of size 2.7 rad/s2.
a. How long does it take for the propeller's angular speed to reach 5.7 rad/s?
b. How many revolutions does it take for the propeller's angular speed to reach 5.7 rad/s?
c. What is the linear speed of the tip of the propeller at 5.7 rad/s?
d. What is the linear acceleration of the tip of the propeller at this point?
e.What is the centripetal acceleration of the tip of the propeller?

### Problem 4

An airplane propeller is rotating at 1900 rev/min.
a. Compute the propeller's angular velocity in rad/s.
b. How long in seconds does it take for the propeller to turn through 30.0 degrees?

### Problem 5

A tire on a rim rolls along a level surface from A to B. The rim moves from C to D and is always in contact with line CD. Since both travel the same distance and the same number of rotations, how can the circumference of the rim not be the same as the circumference of the tire? A rolling tire is an example of rotational motion.

### Problem 6

A disk with a 1.0-m radius reaches a maximum angular speed of 18 rad/s before it stops 35 revolutions (220 rad) after attaining the maximum speed. how long did it take the disk to stop?

### Problem 7

A wagon with wheels having diameter d = 123.0 cm accelerates from rest to 14.5 km/hr in 13.3 s. What is the angular acceleration of the wheels?

### Problem 8

How many revolutions does a disc make in in 5.44 seconds accelerating from 0 to 7.598 thousand rpm?

### Problem 9

A wagon's wheels accelerate at 78.1 rad/s2. If the diameter of wheels is 5.62 inches, what is the wagon's acceleration?

### Problem 10

A truck accelerates from 48 miles/hour to 74 miles/hour through 0.244 miles. What was the angular acceleration of the 3.82 foot diameter wheels?

### Problem 11

Linear Acceleration and Angular Acceleration are related by ...

### Problem 12

A drill bit rotating at 3600 rev/min rotates through 50 revolutions while coming to rest. Find the drill's angular acceleration.

### Problem 13

A 10 inch diameter disk with a nick on its rim moves from rest to an angular speed of 78 rev/min in 3 sec. What is the tangential acceleration of the nick? What is the tangential acceleration of the nick one second after the disk starts to accelerate? When the disk is reaches full speed, what is the tangential velocity of the nick?