Angular Momentum of a sanding disk

In summary, a sanding disk with rotational inertia 1.22x10^-3 kgm^2 attached to an electric drill with a torque of 15.8 Nm will have an angular velocity of 427m/s after 33.0ms. To convert this to revolutions per minute, we can use the conversion factor of 2pi radians per revolution, giving us an angular velocity of 4092 revolutions per minute.
  • #1
Destrio
212
0
A sanding disk with rotational inertia 1.22x10^-3 kgm^2 is attached to an electric drill whose motor delivers a torque of 15.8 Nm
a) find angular momentum
b) find angular speed of the disk 33.0ms after the motor is turned on.

L = Iω
τ = Iα

we can find angular acceleration with what we are given α = τ/I
but I'm completely stumped on how to find L without having time.
any hints?

thanks
 
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  • #2
Here's a hint: You are given the time! :smile:
 
  • #3
Doc Al said:
Here's a hint: You are given the time! :smile:

lol man I stared at that over and over again and thought, "I must be misreading this...wheres the trick?"

But seriously, yes you are given the time. its "33.0ms" part
 
  • #4
Haha, thanks
I realized from that that I can use the time to solve the first part of my problem.

L = Iω

L =τω/α
ω = αt
L =τt

that works

τt = Iω
ω = τt/I
which gives me 427m/s
but i need the answer in rev/min
im okay with seconds to minutes, but how do i convert meters to revolutions?
2pi?
 
  • #5
If you can find its angular acceleration, then ( just like linear kinematics... ) its angular velocity is equal to its angular acceleration multiplied by the duration of the acceleration.
 
  • #6
Destrio said:
τt = Iω
ω = τt/I
which gives me 427m/s
The units for ω are radians/sec, not m/s. One revolution equals [itex]2 \pi[/itex] radians.
 
  • #7
woo i got it!

thanks
 

1. What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is the product of an object's moment of inertia and its angular velocity.

2. How is angular momentum calculated?

Angular momentum is calculated by multiplying an object's moment of inertia (a measure of its resistance to rotational motion) by its angular velocity (the rate at which it rotates).

3. How does a sanding disk's angular momentum change?

A sanding disk's angular momentum can change when there is a change in its moment of inertia or angular velocity. For example, if the disk's mass distribution changes or its rotational speed changes, its angular momentum will also change.

4. What is the conservation of angular momentum?

The conservation of angular momentum states that the total angular momentum of a system remains constant, as long as there are no external torques acting on the system. This means that if one part of a system increases its angular momentum, another part must decrease its angular momentum by the same amount.

5. How is angular momentum related to rotational kinetic energy?

Angular momentum and rotational kinetic energy are related through the moment of inertia. The moment of inertia is a factor in both equations, and a change in one will result in a corresponding change in the other. This means that an increase in the moment of inertia will result in a decrease in both angular momentum and rotational kinetic energy.

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