For the object in the preceding problem, what magnitude torque is necessary to give the object an angular acceleration of 1.5 rad/s^2

a) along the x-axis?
b) along the y-axis?
c) along the z-axis (perpendicular to the page, passing through the origin)?

Help please! Use the correct equation and then plug the numbers into that equation for each problem

To determine the magnitude of torque required for the object to have an angular acceleration of 1.5 rad/s^2 along each axis, we can use Newton's second law for rotational motion. According to this law, the torque τ acting on an object is equal to the product of its moment of inertia I and angular acceleration α:

τ = I * α

We need to determine the moment of inertia for each axis of rotation and then use the given angular acceleration to calculate the torque.

a) Along the x-axis:
The moment of inertia for an object rotating about the x-axis depends on the object's mass distribution. If the mass distribution is known, the moment of inertia can be calculated. Let's assume the object's moment of inertia about the x-axis is given as Ix.

The torque acting along the x-axis would be:
τx = Ix * α

b) Along the y-axis:
Similar to the x-axis, the moment of inertia for an object rotating about the y-axis depends on the mass distribution. Let's assume the object's moment of inertia about the y-axis is given as Iy.

The torque acting along the y-axis would be:
τy = Iy * α

c) Along the z-axis:
The moment of inertia for an object rotating about the z-axis is typically given by the parallel-axis theorem. Let's assume the object's moment of inertia about its center of mass is Icom, and its perpendicular distance from the center of mass to the z-axis is r.

The moment of inertia about the z-axis would be:
Iz = Icom + m * r^2

where m is the mass of the object. As the problem states the z-axis passes through the origin, the perpendicular distance from the origin to the center of mass is equal to r.

The torque acting along the z-axis would be:
τz = Iz * α

Once you have determined the appropriate moment of inertia for each axis, simply substitute the given angular acceleration α into the respective equation to calculate the torque τ for each case.