Dynamics Quiz 3

A rigid body is a collection of particles whose collective motion keeps all particles at constant distances apart.

True

The motion of a rigid body, at any moment in time, can be described in terms of the instantaneous direction of translation and speed of some particle in the body and an instantaneous axis of rotation and angular speed of the body as a whole, all of which may change with time.

True

The angular velocity of a rigid body is a vector quantity whose direction is parallel to the instantaneous axis of rotation of the body

True

The vector between any two particles in a rigid body is a constant vector relative to any observer

False

If omega is the angular velocity of a rigid body and e is a dimensionless direction that points from one particle on the body toward another, then

de/dt = e cross omega

False

The difference between the velocities of two particles in a rigid body is perpendicular to its angular velocity

True

At a moment that a rigid body has zero angular velocity, a nonzero difference between the accelerations of two particles in the body must be perpendicular to the vector between the particles

True

If the angular velocity of a rigid body is perpendicular to the velocity of all particles in the body, then the body must be in planar motion

True

If a rigid body is in planar motion, its angular velocity and angular acceleration are parallel

True

If the angular velocity and acceleration of a rigid body are parallel at any moment in time, then it must be in planar motion

True

If a rigid body is in planar motion with nonzero angular speed, the ratio of the speeds of any two particles on the body equals the ratio of their distances to a point in the plane, independent of the choice of particles

True

If a rigid body rotates about a fixed axis, all particles in the body move along paths with constant curvature

True

If an inextensible cord is wrapped around a rigid pulley, then a condition of no slip means that the cord cannot be unwrapped

False

If an inextensible cord is wrapped around a rigid pulley, the velocity of the particle on the cord where it leaves the pulley can have nonzero components both tangentially and perpendicularly to the pulley’s perimeter

True

If an inextensible cord is wrapped around a rigid pulley and has a free segment that is in tension along a fixed direction, the speed of any point on the segment must equal omega R, where omega is the angular speed of the pulley and R is its radius

True

For two objects in sustained no slip contact, the velocities of the contacting particles on both objects must be equal

True

For a planar rigid body rolling without slip against a surface, the velocity at any particle in the body is perpendicular to a line connecting the particle to the point of no-slip contact

True

For a planar rigid body rolling without slip against a flat surface, every particle in the body must move in a circular path

False