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DISCUSSION THREAD
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DISCUSSION THREAD
At first read through, the motion of the disk rolling on the translating wedge looks complicated. It turns out not be be so complicated; rather, it can be described through a straight-forward expression of the rigid body kinematics equation for the disk. If we focus our attention on the disk by itself, we know the direction of of motion for two points on the disk: point O moving in the negative y-direction with an unknown speed of vO, and since point C does not slip on the wedge, C moves in the negative x-direction with a known speed of vC = vA. This is as shown in the following figure.
From this, we can write the following vector kinematics equation for the disk:
vC = vO + ω x rC/O
Although this is a single vector equation, it is made up of two scalar equations due to its x- and y-components. These two scalar equations are in terms of two unknowns: ω and vO. For Part (a), solve these two equations.
For Part (b), you can now write the rigid body kinematics equations relating points O and B in order to find the vector velocity expression for point B:
vB = vO + ω x rB/O.
Is the velocity of the ball at the point of contact with the ramp in the i and j direction or just i?
No slip says it has the same velocity as the wedge. The wedge moves only in x.
The velocity of the ball at the point of contact is only in the i direction. This is because if the ball only rolls and not slips it stay in the same position without moving downwards. If we consider this point on the ball the velocity in the i direction is zero. This is because the total velocity at the bottom of the ball where the ball is in contact with the slope is -R*omega + R*omega, where -R*omega is the rotational velocity of the bottom point, and the R*omega is the translational velocity of the center of mass.
On the other hand if we consider that point on the slope it moves with Va as all the points on the slope move with Va in the i direction.
Should your angular velocity be positive or negative? I know that V_o is in the negative j direction and V_b is in the positive i direction but it one always seems to be wrong mathematically when I change the sign of the angular velocity.
Let the mathematics tell you if the rotation is in the positive or negative k-direction.
Doesn’t the disk’s center also have velocity in the horizontal component? Or is this problem just focusing on the vertical component.
I think for this particular problem Vo is only in the negative j direction since that’s how it’s shown on the diagram.
This is a problem in kinematics. We do not know all of the forces that are acting on the system. What is know is the the forces are such that the wedge is moving with a speed of v_A along the horizontal surface, and that O has a velocity that is purely in the y-direction.
Is the angle between Vo and Rc/o equivalent to theta?
The things on which you need to focus for this problem are:
* C is pointing in the negative x-direction, as shown in the figure in the Hints.
* The vector of r_O/C is the vector pointing from C to O; that is, this vector is off at an angle to theta with respect to the y-axis.
Would the omega values be constant on the entire disk? So if i calculated and found the value for W_oc, would that also equal to W_ob?
Angular velocity is a property of the motion of a rigid body. When writing the rigid body kinematics equation for a body, it applies to ANY two points on the body.
Same goes for angular acceleration, which is also a property of the motion of the rigid body.