Rotational Kinetics

Problems

Problem 2.1:

A jet engine, starting from rest, is accelerated at a rate of 5 rad/s². After 15 seconds, what is the angular velocity of the engine? What is the total angular displacement over this period of time?

[Solution]

Problem 2.2:

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?

[Solution]

Problem 2.3:

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/s². What is the final angular velocity of the merry-go-round?

[Solution]

Problem 2.4:

An object moves in a circle of radius 2 m with instantaneous angular velocity of 5 rad/s and angular acceleration of 4 rad/s². What is the magnitude of the linear acceleration felt by the object?

[Solution]

Problem 2.5:

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 P.1: 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.

[Solution]

Solution for Problem

Recall that

. We can assume that the angular velocity is constant, so we can use this equation to solve our problem. Each revolution corresponds to an angular displacement of 2π radians. Thus 100 revolutions corresponds to 200π radians. Thus:

ω =

= 40π rad/s = 125.7 rad/s

Problem 2.6:

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?

[Solution]

Problem 2.7:

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?

[Solution]

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Rotational Kinematics