Rotational motion and angular displacement

[invadertak]

Homework Statement

A baton twirler throws a spinning baton directly upward. As it goes up and returns to the twirlers hands, the baton turns through four revolutions. Ignoring air resistance and assuming that the average angular speed is 1.80 rev/s, determine the height to which the center of the baton travels above the point of release.

Homework Equations

The Attempt at a Solution

I know that the total angular displacement is 25.13 radians and, therefore, the angular displacement the baton moves through to reach the maximum height is 12.565 radians. The anguar velocity which the baton experiences is 11.31 radians/sec. The total time of the trip is 2.2 seconds and the time to reach the top is 1.1 sec. Will the height reached by the centre of the baton be the radius? I can't quite get my mind around this angular displacement and velocity. I'm really stuck on this question.

 

[Doc Al]

I know that the total angular displacement is 25.13 radians and, therefore, the angular displacement the baton moves through to reach the maximum height is 12.565 radians. The anguar velocity which the baton experiences is 11.31 radians/sec. The total time of the trip is 2.2 seconds and the time to reach the top is 1.1 sec.

Good. (FYI, there's no need to use radians. You are told it rotates through 4 revolutions at a speed of 1.8 rev/sec. So how long does it take to spin through those 4 revolutions?)

Will the height reached by the centre of the baton be the radius? I can't quite get my mind around this angular displacement and velocity.

Now that you have the time it takes for the baton to reach its highest point, find the height it reaches by treating it like any other tossed object. If you threw an apple straight up in the air and it took 1.1 seconds to reach its highest point, how high did it reach?

 

[invadertak]

Thanks. I thought about using straightforward projectile motion, but I'd just started the section on rotational motion and it seemed a bit soon in the exercises to start using anything other than the formulas for angular displacement and velocity.