Center of Mass
Rotational Kinematics
While units of rotation may look new and different, they are related to traditional kinematic notation. Translational distance is related to the theta of a rotation, translational velocity is related to the omega, or angular velocity, and the translational acceleration is related to alpha, or the angular acceleration.
Translational distance / radius of rotating object = number of radians in a rotation Translational distance / (radius of rotating object * 2 * π) = Degrees of the rotation Angular velocity * radius of rotating object = translational velocity angular acceleration * radius of rotating object = translational acceleration These substitutions can be used in traditional kinematic equations to gain new equations for solving problems related to rotational kinematics. |
Torque
Rotational Inertia and Rotational Energy
torque_gif_attempt_3.gif | |
File Size: | 1561 kb |
File Type: | gif |
In this gif, there are 4 objects rolling down an incline. The first two are rings, of which one is hollow. The hollow ring accelerates from rest at a lower rate than the normal ring, but why?
The reason for this lies in the equations: I = k * m * r^2 The rotational inertia of an object is equal to a constant multiplies by its mass and its radius squared. Tnet = I * alpha The net torque is equal to the rotational inertia multiplied by the angular acceleration. The hollow ring has a higher radius, in that more mass is spread out from the center of mass, and therefore will have a higher value of I. All of the objects in the track have the same net torque. The reason for this is because the only external force causing a torque on the balls is gravity, and gravity is constant throughout all of the balls. Since the net torque is constant for all of the balls, and I is higher for the hollow ring with the higher radius, then the alpha, or angular acceleration of the ball must be lower. The higher the angular acceleration, the faster the ball will roll down the track, and since all of the balls have the same radius and are not slipping, then the distance that needs to be traveled is constant in all four cases. This explains why the hollow ring is the slowest object rolling down the incline. |
ANSWERS - B, A, ABCDFH, C
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