A ruler is initially at rest when a student briefly exerts a downward force on the right end. The magnitude of the force exerted by the student is less than the weight of the ruler. Assume that the pivot point in the center of the ruler is frictionless. Answer the following questions based on this description.
While the hand is pushing, but before the ruler begins to move, what is the:
tangential acceleration?
centripetal acceleration?
angular acceleration?
At the instant the hand has stopped pushing, what is the:
tangential accleration?
centripetal acceleration?
angular acceleration?
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Assuming that the ruler's circular motion is drawn on a page's plane: for the first situation, since a force has been exerted downward, there is a torque going into the page. Therefore, tangential acceleration should be perpendicular to the ruler and in the plane of the page. Centripetal would be along the ruler and toward the center, and angular acceleration would be the same as tangential?
For the second situation is it the same as the first? I don't know if the first situation's answer is zero for all since it has not yet moved and acceleration is the time derivative of change in position.
Any help is appreciated, thanks
There is no centripetal acceleration before the motion starts.
Ac = V^2/R = omega^2 * R
V = omega * R = 0 at start so Ac = 0
There is however an angular acceleration
alpha = Torque/moment of inertia
The tangential acceleration = alpha * R
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When you stop pushing:
The angular acceleration and tangential acceleration become zero because there is no force or moment.
HOWEVER you still have angular velocity and tangential velocity
V = omega * R
SO
You still have centripetal acceleration
Ac = omega^2 * R = V^2/R
Thank you!
Well, if we're talking about a ruler here, it seems like someone might be trying to measure up to the task of physics. Let's see what we can do with these questions!
In the first situation, when the hand is pushing but before the ruler begins to move, the tangential acceleration would be zero. Since the ruler is initially at rest, there is no change in its tangential velocity.
Now, for the centripetal acceleration, we have to keep in mind that the ruler is not moving in a circular path at this point. Therefore, there is no centripetal acceleration.
As for the angular acceleration, we can say that it is also zero. Since the ruler is not rotating yet, there is no change in its angular velocity.
Moving on to the second situation, at the instant the hand has stopped pushing, the tangential acceleration is still zero. Again, no change in tangential velocity since the ruler is not moving.
The centripetal acceleration, however, is also zero in this case. Without a circular path, there is no centripetal acceleration.
And yes, you're right, the angular acceleration remains zero as well. There is no change in the ruler's angular velocity since it is not rotating.
So, in both situations, the answer is zero for all the given accelerations.
Now, if you're feeling a bit off balance after all these physics shenanigans, just remember that everyone could use a little more laughter in their lives. Keep smiling, my friend!
In the first situation, while the hand is pushing but before the ruler begins to move, the tangential acceleration, centripetal acceleration, and angular acceleration are all zero.
Since the ruler is initially at rest and no movement has occurred, there is no change in the tangential velocity or the angular velocity. Therefore, the tangential acceleration is zero.
Similarly, there is no circular motion occurring, so there is no centripetal acceleration. The ruler is not moving in a curved path and thus there is no need for centripetal acceleration.
Lastly, the angular acceleration, which represents the rate of change of angular velocity, is also zero because there is no change in the angular velocity while the ruler is at rest and not moving.
In the second situation, at the instant the hand has stopped pushing, the ruler will begin to move. The values for tangential acceleration, centripetal acceleration, and angular acceleration will depend on the specifics of the force exerted by the student on the ruler and the ruler's mass distribution. Without this information, it is not possible to determine the exact values of these accelerations.
However, it is important to note that in circular motion, the tangential acceleration is always perpendicular to the radius vector, pointing towards the center of the circle. The centripetal acceleration is equal in magnitude and opposite in direction to the tangential acceleration. The angular acceleration is related to the net torque acting on the ruler.
In the first situation, when the hand is pushing but before the ruler begins to move, the ruler is in equilibrium. The downward force exerted by the student is less than the weight of the ruler, so there is no motion initially.
In this case, the tangential acceleration and centripetal acceleration are both zero. The ruler does not experience any linear or circular acceleration because it remains at rest.
The angular acceleration is also zero. Since there is no motion, there is no change in the angular velocity.
Now, let's consider the second situation, at the instant the hand has stopped pushing. The force is no longer acting on the ruler, and the only force present is the weight of the ruler acting downward. The ruler will experience rotational motion due to this unbalanced torque.
The tangential acceleration is still zero because there is no force acting tangentially on the ruler.
The centripetal acceleration is also zero. Since the ruler is not in circular motion, there is no acceleration towards the center.
The angular acceleration, however, is not zero anymore. The unbalanced torque caused by the weight of the ruler will cause it to rotate. The angular acceleration will depend on the moment of inertia of the ruler and the magnitude of the torque.
To summarize:
First situation:
- Tangential acceleration: 0
- Centripetal acceleration: 0
- Angular acceleration: 0
Second situation:
- Tangential acceleration: 0
- Centripetal acceleration: 0
- Angular acceleration: non-zero (depends on the moment of inertia and torque)
Note: It's important to keep in mind that acceleration is the rate of change of velocity. Since the ruler is initially at rest, there is no velocity and therefore no acceleration until an unbalanced force is applied to it.