Kinematics of Rigid Bodies - Review Problems

RP4-1) Explain the difference between relative and absolute velocities.

RP4-2) Consider a rigid body undergoing pure rotation. Every point on that body moves in a path around the fixed axis.

RP4-3) Points on a body undergoing pure rotation that are at different distances from the fixed axis have different velocities.

RP4-4) Points on a body undergoing pure rotation that are at different distances from the fixed axis have different angular velocities.

RP4-5) Rigid-body motion has two components. What are they?

RP4-6) The velocity of any point on a body experiencing fixed-axis rotation is v = r ω. What direction is this velocity? The velocity is in the direction.

RP4-7) Consider the velocity equation for point B on a rigid body (vB = vA + vB/A = vA + ω x rB/A). Which component accounts for the translation of the body and which accounts for the rotation of the body about A?

Rotation

Translation

RP4-8) How can the instantaneous center of zero velocity make our calculations easier?

RP4-9) The velocity of a point on a rigid body is always perpendicular to the line that connects the point to the .

RP4-10) Consider two points (A, B) on a rigid body and the instantaneous center of zero velocity (IC). If point A is twice as far away from the IC as B is, what is the equation relating vA to vB?

RP4-11) A wheel of radius r is rolling while slipping at the point of contact between the wheel and ground. The speed of the wheel's center is v = rω.

RP4-12) Consider the equation for the acceleration of point B on a rigid body (aB = aA + α x rB/A - ω2rB/A ). Which component(s) accounts for the translation of the body, which component(s) accounts for the rotation of the body?

Rotation

Translation

RP4-13) The acceleration of an IC is generally zero.

RP4-14) A cord is wrapped around a cylinder of radius 0.2 meters, as shown in the figure. Starting from rest, the cord is pulled downward with a constant acceleration of 10 m/s2. Determine the angular acceleration and angular velocity of the disk after it has completed 10 revolutions.

RP4-15) When the slider block C is in the position shown, the link AB has a clockwise angular velocity of 2 rad/s. Determine the velocity of block C at this instant. The length of link AB is 1 meter and the length of link BC is 0.7 meters.

vB = i j m/s

vC = m/s

RP4-16) A cord is wrapped around the inner hub of a wooden spool. The end of the cord is attached to a fixed horizontal support. The spool is released and allowed to fall under the influence of gravity as the cord unwinds. Assuming that the spool does not sway back and forth, determine the velocity of point A for the instant shown where the speed of the center of the spool (point O) has reached 5 ft/s.

vA = i + j ft/s

RP4-17) The ball shown rolls without slipping and has an angular velocity and angular acceleration of 6 rad/s and 4 rad/s2, respectively, with the directions shown in the figure. Determine the acceleration of point B at this instant.

vIC = 0

aIC = 0

aO = m/s2

aB = i + j m/s2