Pin P is attached to the wheel and slides in a slot cut in bar BD. The wheel rol
ID: 3162872 • Letter: P
Question
Pin P is attached to the wheel and slides in a slot cut in bar BD. The wheel rolls to the right without slipping with an angular velocity of to rad/s and an angular acceleration of a rad/s^2. Reference Frames: R - ground, R_1 -wheel, R_2 - rod BD. All motion takes place in the plane of the paper. Describe what the assumption of no slip means, i.e., for the two points in contact, one on each body, what must be the same for each of those points for there to be no slip between them? What is R_v^c? Point C is the point on the wheel in contact with the ground. The wheel does not slip on the ground. What is R_v^A? The wheel does not lose contact with the ground. What does this tell you about the relationship between the rotational motion of a wheel and the translational motion of its geometric center when the wheel rolls on the ground without slipping? Using the R and R_1 reference frames, write an expression for^R_v^p. Using the R and R_2 reference frames, write an expression for^R_v^p. Equate the two expressions in (4) and (5). Given values for x and theta, what are the unknowns in that equation? Can you solve for all the unknowns'? Explain.Explanation / Answer
1. Assumption of no slip means that for two different points on tweo different bodies in contact, the thwo different points in contact should have relative velocity = 0
hecne both the points have same velocity
2. Vrc = 0 [ as C is in contact with ground, and has to obey no slip condidiotn and the ground is at rest]
3. Vra = wR
where w = wo + alpha*t [ wo is initial angular velocity and alpha is angular accelration and t is the time after the initial angular velocity was measured]
Vra = (wo + alpha*t)R
this tells us that
1, the centre of the rolling wheel moves in a steaight line with a linear velocity which is aproduct of the angular velocity of the wheel and its radius
2. instantaneously speaking the centre of the disc is in pure rotation wrt to the point of contact on the ground which is instantaneously at rest
4. Vrp = V1p - Vr1
assuming distance of the pin from the centre of the wheel to be z
V1p = w*z(cos(theta)i - sin(theta)j) = (wo + alpha*t)*z(cos(theta)i - sin(theta)j)
Vr1 = wR i ( laong x axis)
so
Vrp = (wo + alpha*t)*z(cos(theta)i - sin(theta)j) - wR i