# Rotational motion

#### tupldy

1. The problem statement, all variables and given/known data

A wheel decellerates from 100 rpm in 10 sec. Find angular acceleration, torque and the force torque is producing on a fixed object.
The wheel has a radius of .0025m and a mass of 50kg.

2. Relevant equations
T=Ia
a=ra
T=dL/dt

3. The attempt at a solution

The first thing I did was change rpm to rad/sec which gave me 10.5 rad/sec.
for angular acceleration i used: a=ra-> .0025*10.5/10 which gave me
For torque i used 1/2*50*.0025^2*1.05 which gave me .00016 kgm^2.
I am not sure where to go with this now, or even if I am headed in the right direction. Any suggestions would be greatly appreciated.

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#### Hootenanny

Staff Emeritus
Gold Member
You have not correctly found the angular acceleration. The definition of angular acceleration is;

$$\alpha = \frac{d\omega}{dt}$$

#### tupldy

wouldn't the dw in this case just be the 10.5 rad/sec divided by 10(then number of seconds it takes for the wheel to stop?

#### Doc Al

Mentor
I assume you mean:
$$a = r \alpha$$
This relates angular acceleration to linear acceleration.
The first thing I did was change rpm to rad/sec which gave me 10.5 rad/sec.
OK.
for angular acceleration i used: a=ra-> .0025*10.5/10 which gave me
You are mixing up angular and linear acceleration. All you need is angular acceleration.

#### tupldy

yes, your formula for acceleration is the one i meant. I understand that dw/dt is angular acceleration, so do i just not multiply by the radius? I am very confused here.

#### Doc Al

Mentor
I understand that dw/dt is angular acceleration, so do i just not multiply by the radius?
Correct. You would only multiply by the radius if you needed the linear acceleration (units: m/s^2) of a point on the rim of the wheel.

#### tupldy

ok so now that i know torque of the wheel is .00016kgm^2 and angular acceleration is 1.05 rad/sec^2. How do i figure out what the force is that the torque of the wheel is producing on a fixed object, say someone's head for example?

#### Doc Al

Mentor
If you assume that the torque is created by a force applied tangentially to the edge of the wheel, what force is required to generate that torque? (What's the definition of torque?)

#### tupldy

Torque = R xF or Torque = I alpha or Torque = dL/dt.
I understand that these are the formulas for torque, I am just not sure which one I am supposed to use.

#### tupldy

I decided to try T=R x F. What I got was that the torque of the wheel is equal to the radius times the unknown F times the sin90.

.00016=.0025F

F=.064N
Does this look right to you?

#### Doc Al

Mentor
Well, what are you trying to find? Which formula relates to that quantity?

#### tupldy

I am trying to find the force the torque exerts on the object The formula I used was Torque = R x F.

#### Doc Al

Mentor
I decided to try T=R x F.
Wise choice, since that's the only one that has force in it.

What I got was that the torque of the wheel is equal to the radius times the unknown F times the sin90.

.00016=.0025F

F=.064N
Does this look right to you?
Looks OK to me.

#### tupldy

Great thank you so much for all your help. :0)

"Rotational motion"

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