Rotation(Theory questions) Flashcards
A clock is mounted on the wall. As you look at it, what is the direction of the angular velocity
vector of the second hand?
The second hand rotates clockwise, so by the right-hand rule, the angular velocity vector is into
the wall.
A baseball bat is swung. Do all points on the bat have the same angular velocity? The same
tangential speed?
If a rigid body has a constant angular acceleration, what is the functional form of the angular
velocity in terms of the time variable?
straight line, linear in time variable
Explain why centripetal acceleration changes the direction of velocity in circular motion but
not its magnitude.
The centripetal acceleration vector is perpendicular to the velocity vector
If the angular acceleration of a rigid body is zero, what is the functional form of the angular
velocity?
constant
Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it
experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) the plate
starts to spin faster? (b) The plate rotates at constant angular velocity? (c) The plate slows to a
halt?
a. both; b. nonzero centripetal acceleration; c. both
A solid sphere is rotating about an axis through its center at a constant rotation rate. Another
hollow sphere of the same mass and radius is rotating about its axis through the center at the
same rotation rate. Which sphere has a greater rotational kinetic energy?
The hollow sphere, since the mass is distributed further away from the rotation axis.
A discus thrower rotates with a discus in his hand before letting it go. (a) How does his
moment of inertia change after releasing the discus? (b) What would be a good approximation to
use in calculating the moment of inertia of the discus thrower and discus?
a. It decreases. b. The arms could be approximated with rods and the discus with a disk. The
torso is near the axis of rotation so it doesn’t contribute much to the moment of inertia.
The moment of inertia of a long rod spun around an axis through one end perpendicular to its
length is mL^2 / 3. Why is this moment of inertia greater than it would be if you spun a point mass
m at the location of the center of mass of the rod (at L/2) (that would be mL^2 / 4 )?
Because the moment of inertia varies as the square of the distance to the axis of rotation. The
mass of the rod located at distances greater than L/2 would provide the larger contribution to
make its moment of inertia greater than the point mass at L/2.
What three factors affect the torque created by a force relative to a specific pivot point?
magnitude of the force, length of the lever arm, and angle of the lever arm and force vector
Can a set of forces have a net torque that is zero and a net force that is not zero?
yes
When reducing the mass of a racing bike, the greatest benefit is realized from reducing the
mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations
than would an identical reduction in the mass of the bicycle’s frame?
The moment of inertia of the wheels is reduced, so a smaller torque is needed to accelerate them.
A track star runs a 400-m race on a 400-m circular track in 45 s. What is his angular velocity
assuming a constant speed?
0.14 rad s
On takeoff, the propellers on a UAV (unmanned aerial vehicle) increase their angular
velocity for 3.0 s from rest at a rate of ω = (25.0 )rad s t where t is measured in seconds. (a)
What is the instantaneous angular velocity of the propellers at t = 2.0s ? (b) What is the angular
acceleration?
25.0 rad/s
A wheel has a constant angular acceleration of Starting from rest, it turns
through 300 rad. (a) What is its final angular velocity? (b) How much time elapses while it turns
through the 300 radians?
a) 54.8rad s
b) 11.0 s
A rod of length 20 cm has two bead attached its ends. The rod with beads starts rotating from
rest. If the bead are to have a tangential speed of 20 m/s in 7 s, what is the angular acceleration of
the rod to achieve this?
28.6rad s
A child with mass 40 kg sits on the edge of a merry-go-round at a distance of 3.0 m from its
axis of rotation. The merry-go-round accelerates from rest up to 0.4 rev/s in 10 s. If the
coefficient of static friction between the child and the surface of the merry-go-round is 0.6, does
the child fall off before 5 s?
235.2 N, so child does not fall of yet
