What kind of motion does a constant, non zero torgue produce on an object mounted on an axle: choices constant rotational speed, constant rotational acceleration, increasing rotational acceleration or decreasing rotational acceleration.
constant rotational acceleration
A constant, non-zero torque produces a constant rotational acceleration on an object mounted on an axle. To understand why, we need to look at the relationship between torque, moment of inertia, and angular acceleration.
Torque (τ) is defined as the product of the applied force (F) and the perpendicular distance (r) from the axis of rotation to the point where the force is applied. Mathematically, it can be expressed as τ = F * r.
The moment of inertia (I) represents an object's resistance to changes in its rotational motion. It depends on the mass distribution and the axis of rotation. The greater the moment of inertia, the more effort (torque) is required to change the rotational motion of the object.
Angular acceleration (α) describes how quickly an object's angular velocity changes over time. It is related to torque and moment of inertia through the equation τ = I * α, where τ is torque, I is moment of inertia, and α is angular acceleration.
In the given scenario, a non-zero torque means that there is a force applying a continuous rotational effort on the object. Since the torque is constant, this means that the torque value remains the same over time.
According to the equation τ = I * α, if the torque is constant, and the moment of inertia (I) remains constant for the object and its axle, then the angular acceleration (α) must also remain constant. Therefore, a constant, non-zero torque will produce a constant rotational acceleration.
So, the correct answer is "constant rotational acceleration."