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

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 seconds

convert any units as necessary

please 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 them

Torque = Moment of Inertia * Angular Acceleration
Angular Acceleration = Difference in Angular Velocity / Difference in Time

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rl.bhat
Homework Helper
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.

rl.bhat
Homework Helper
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

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