# Rotational Kinetics

### Problems

Problem :

A jet engine, starting from rest, is accelerated at a rate of 5 rad/ s 2 . After 15 seconds, what is the angular velocity of the engine? What is the total angular displacement over this period of time?

Problem :

Most hurricanes in the northern hemisphere rotate counterclockwise, as seen from a satellite view. In what direction does the angular velocity vector of a hurricane point?

Problem :

A merry-go-round is traveling initially with an angular velocity of 5 rad/s. A child pushes the merry-go-round over 10 revolutions, causing the merry-go-round to accelerate at a constant rate of 1 rad/ s 2 . What is the final angular velocity of the merry-go-round?

Problem :

An object moves in a circle of radius 2 m with instantaneous angular velocity of 5 rad/s and angular acceleration of 4 rad/ s 2 . What is the magnitude of the linear acceleration felt by the object?

Problem :

In lacrosse, a typical throw is made by rotating the stick through an angle of approximately 90 o , then releasing the ball when the stick is vertical, as shown below. If the stick is at rest when horizontal, the length of the stick is 1 meter, and the ball leaves the stick with a velocity of 10 m/s, what angular acceleration must the stick experience?

Figure %: The lacrosse stick is accelerated through an angle of 90 o . At point A, the stick is at rest. At point B, the ball is released.

Problem :

A car, starting from rest, accelerates for 5 seconds until its wheels are moving with an angular velocity of 1000 rad/s. What is the angular acceleration of the wheels?

Problem :

A merry-go-round is accelerated uniformly from rest to an angular velocity of 5 rad/s in a period of 10 seconds. How many times does the merry-go-round make a complete revolution in this time?

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