Question

Help me pleaseee, it’s due today: Two people push on a large gate as shown on the view from above in the diagram. If the moment of inertia of the gate is 90 kgm2, what is the resulting angular acceleration of the gate?

Answer 1

the angular acceleration of the gate is approximately 1.61
`(rad)/(s^2)`

Step-by-step explanation:

Recall the formula that connects the net torque with the moment of inertia of a rotating object about its axis of rotation, and the angular acceleration (similar to Newton's second law with net force, mass, and linear acceleration):

`\sum \tau_1=I\,\alpha`

In our case, both forces contribute to the same direction of torque, so we can add their torques up and get the net torque on the gate:

`\tau_(net)=(20*2+30*3.5) \,N\,m=145\,\,N\,m`

Now we use this value to obtain the angular acceleration by using the given moment of inertia of the rotating gate:

`\sum \tau_1=I\,\alpha\\145\,\,N\.m=(90\,\,kg\,m^2)\,\alpha\\\alpha= (145)/(90) (rad)/(s^2) = 1.61\, (rad)/(s^2)`