Angular Motion: Solving for Velocity & Acceleration

[Kevin1199959]

Homework Statement

A wheel 1m in diameter is rotating on a horizontal plane in the clockwise direction with an angular speed of 115 rpm. It's angular acceleration is 18 rad/s²

A) What is the angular velocity (magnitude and direction) after 6 seconds
B) What is the tangential velocity of a point on the rim of the wheel at 6 seconds
C) What is the resultant acceleration of a point on the rim at 6 seconds

Homework Equations

2pie ; 1 rev

The Attempt at a Solution

I don't know how to find the answer

 

[tiny-tim]

Hi Kevin1199959!

(have a pi: π )

You can use the same constant acceleration equations as for linear motion.

And linear displacement speed and acceleration are r times the angular version.

 

[Kevin1199959]

Hi Kevin1199959!

(have a pi: )

You can use the same constant acceleration equations as for linear motion.

And linear displacement speed and acceleration are r times the angular version.

Lol, thanks again :P Btw, where do you get the signs from? So that you won't have to give them to me every time...

Soo;
A) 18*6/2π+115 = 117.86 rpm? But it sais magnitude and direction... do i actually have to give a direction?

B) r*117.86= 117.86 revolutions = tangential velocity?

C) ?!?

Please elaborate... I'm really lost!

 

[jhae2.718]

The angular velocity is a vector* that is perpendicular to the direction of rotation (see the first image on Wikipedia's article: http://en.wikipedia.org/wiki/Angular_velocity)

You can use a sort of right hand rule to find the direction; curl your hand in the direction of rotation and then the vector points along your thumb. *technically a pseudovector, but let's forget about that...

 

[Kevin1199959]

The angular velocity is a vector* that is perpendicular to the direction of rotation (see the first image on Wikipedia's article: http://en.wikipedia.org/wiki/Angular_velocity)

You can use a sort of right hand rule to find the direction; curl your hand in the direction of rotation and then the vector points along your thumb.


*technically a pseudovector, but let's forget about that...

I'm still lost... can you please explain what i have to do?! Can you give me an example of an answer at least?

 

[tiny-tim]

Hi Kevin1199959!

(just got up :zzz: …)

A) 18*6/2π+115 = 117.86 rpm? But it sais magnitude and direction... do i actually have to give a direction?

How did you get 117.86? (and you only need 3 significant figures anyway)

The way I remember the direction is that anti-clockwise is positive, so the angular velocity is up for anti-clockwise, and down for clockwise.

B) r*117.86= 117.86 revolutions = tangential velocity?

Ah, perhaps I should have specified …

And linear displacement speed and acceleration are r times the angular version, measured in radians. ​

C) ?!?

The "resultant acceleration" is the vector sum of the tangential acceleration and the centripetal acceleration

Btw, where do you get the signs from? So that you won't have to give them to me every time...

On a Mac , you just type them! :tongue2: … for example, µ is alt-m.

On a PC , the only thing you can do is to copy them into a text document for future pasting.