Calculating Torque of a Solid Cylinder

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In summary, the torque acting on the armature can be calculated using the formula T = I α, where I is the rotational inertia and α is the rotational acceleration. To find I, use the formula 1/2 mr^2, where m is the mass and r is the radius. To find α, use the formula a/r, where a is the change in velocity and r is the radius. Once you have both values, multiply them together to find the torque. Alternatively, you can calculate α using the formula ω/t, where ω is the angular velocity (converted from rpm to radians/sec) and t is the time interval.
  • #1
Schu
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I am attempting to the following question:
How large is the torque that act on an armature?

Particulars: (can be approximated as a solid cylinder)
radius of .081 m
length of .124 m
mass of 13.13 kg
Accelerated from REST to operating speed of 3530 rpm in 5.57 second

I know T = F*r
I'm not sure where to start.
 
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  • #2
You are given the mass, the radius, and a change in velocity over a given time interval.

Think of the problem another way:
T = F x r
from Newton's 2nd law: F = m*a
a = dv/dt
so you have: T = m dv/dt x r
start by converting the given velocity into meters per second, then calculating the acceleration. from there it is plug and chug
 
  • #3
Newton's 2nd law - for rotational motion

Schu said:
I know T = F*r
I'm not sure where to start.
You'll need to apply Newton's 2nd law for rotational motion:
[tex]\tau = I \alpha[/tex]

You are given all the information needed to calculate I (the rotational inertia) and [itex]\alpha[/itex] (the rotational acceleration).
 
  • #4
Just to make sure you know that [itex]\tau = r \times F[/itex] not [itex]\tau = F \times r[/itex], it makes a difference. And [itex]||\tau||= rF\sin \phi[/itex]
 
  • #5
Now ya'll have me confused again, I thought I was all set with the first formula,
T = f * r. Now where does Newtons Second Law fit into it to get the rotational movement.

Take me step by step if you would.
Thanks for the help so far
 
  • #6
Good point, Corneo. (But it won't matter for this particular problem.)
 
  • #7
Schu said:
Now ya'll have me confused again, I thought I was all set with the first formula,
T = f * r. Now where does Newtons Second Law fit into it to get the rotational movement.
T = r X F is true, but not helpful in this problem. Are you given the force? No.

This is just the rotational analog to an "F = ma" problem. Instead of m, you calculate I; instead of a, you calculate α. Then apply T = I α.

Give it a shot.
 
  • #8
Ok check to see if I am OK on this;
we know T = I α
I = 1/2 mr^2 and α = a / r
so plug it in
I = (1/2) 13.13 * .081^2 = .043072965
α = (29.9425 / 5.57)/.081 = 66.36633641
Multiply the two together for T and you get 2.8585 Nm

How'd I do??
 
  • #9
Looks good. Note that you can calculate [itex]\omega[/itex] directly from the rpm, then use it to calculate [itex]\alpha = \omega/t[/itex]. Just convert rpm to radians/sec.
 

1. What is torque?

Torque is a measure of the force that causes an object to rotate about an axis. It is calculated by multiplying the applied force by the distance from the axis of rotation to the point where the force is applied.

2. How do you calculate torque for a solid cylinder?

To calculate the torque of a solid cylinder, you will need to know the force applied to the cylinder and the distance from the axis of rotation to the point where the force is applied. The formula for torque is T = F x r, where T is torque, F is the applied force, and r is the distance from the axis of rotation.

3. What units are used to measure torque?

Torque is typically measured in units of newton-meters (Nm) or foot-pounds (ft-lb) in the metric and imperial systems, respectively.

4. How does the shape of a cylinder affect its torque?

The shape of a cylinder does not directly affect its torque. The torque is primarily determined by the force applied and the distance from the axis of rotation. However, the shape of the cylinder can indirectly affect the torque by influencing the distribution of weight and the distance from the axis of rotation to the point where the force is applied.

5. What factors can affect the accuracy of torque calculations for a solid cylinder?

The factors that can affect the accuracy of torque calculations for a solid cylinder include the precision of the measurements for the applied force and distance, the uniformity of the cylinder's shape and weight distribution, and any external forces or factors that may influence the rotation of the cylinder.

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