# Solve for torque? Torque = Moment of Inertia * Angular Acceleration?

• soundengineer
In summary, the wheel has a diameter of 26 inches and weighs 3900 lbs, spinning at 100 MPH. To accelerate it to 109 MPH in 2.0 seconds, a torque of 142.2600984 Slug-ft² is needed. To find torque, convert linear velocity to angular velocity, calculate the moment of inertia, and use the formula T=I*alpha. It is important to include units in calculations, such as converting lbs to slugs for the moment of inertia.
soundengineer
I have a wheel with a diameter of 26 inches that weighs 3900 lbs that is spinning at 100 MPH...
How much torque is needed to accelerate the wheel to 109 mph in 2.0 secondsanswer must be in ft-lbs
convert any units as necessaryplease show me the math so I can learn how to do this..I have a few problems similar to this one and I am trying to learn how to do themTorque = Moment of Inertia * Angular Acceleration
Angular Acceleration = Difference in Angular Velocity / Difference in Time

Convert MPH to ft/s.
Convert linear velocity to angular velocity by using w = v/r
Calculate moment of inertia.
Calculate angular momentum and rate of change of angular momentum.

ok...MPH to feet/sec
100mph = 146.66666667 ft/sec
109mph = 159.86666703 ft/sec

Linear velocity = (159.86666703ft/sec-146.66666667ft/sec)/2 = 6.60000018ft/sec
angular velocity = 6.60000018/3.403392041=1.939241768revolutions = 698.1270365° = 12.18461538radians/sec

correct?

Moment of inertia = Mass * R²(Distance from center of wheel to outside?)? = 3900lbs*(1.08333333ft)² = 4577.083333 lb-ft²

then I'm lost...edit:
do I need to convert lbs to slugs? moment of inertia in slug-ft²?
lbs * 0.03108095004
so 3900* 0.03108095004=121.2157052
Moment of Inertia = 142.2600984 Slug-ft²

or was I right above this?

Last edited:
Yes, convert the weight to mass (slugs) to determine the moment of inertia. Since

$$T=I\alpha$$

and

$$\alpha=\mbox{angular acceleration}$$

You can determine the torque with units of ft-lbs.

Linear velocity = (159.86666703ft/sec-146.66666667ft/sec)/2 = 6.60000018ft/sec
How can this be a velocity?
Change in velocity/time = acceleration. = a.
Anguler acceleration = a/r
Moment of Inertia of the wheel = 1/2*M*R^2

hello friends i like all your post but unit also have its own important so keep given unit at each places so will be more helpful

have u any information about robotic control

## 1. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis.

## 2. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in rotational motion.

## 3. What is angular acceleration?

Angular acceleration is the rate at which an object's angular velocity changes.

## 4. How do you calculate torque?

Torque is calculated by multiplying the moment of inertia of an object by its angular acceleration.

## 5. How is torque used in scientific research?

Torque is used in many scientific fields, such as physics and engineering, to study rotational motion and analyze the forces acting on rotating objects.

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