Physics C II Questions and Answers
Torque is the rotational analogue of
Force
A square piece of plywood on a horizontal tabletop is subjected to the two
horizontal forces shown above. Where should a third force of magnitude 5
newtons be applied to put the piece of plywood into equilibrium
{Down arrow in top left corner}
Diagram + A uniform rigid bar of weight W is supported in a horizontal orientation
as shown above by a rope that makes a 30 degree angle with the horizontal. The
force extorted on the bar at point O, where it is pivoted, is best represented by a
vector whose direction is which of the following?
{arrow up and to the right}
A rod of negligible mass is pivoted at a point that is off center, so that length l1 is
different from length l2. The figures above show two cases in which masses are
suspended from the ends of the rod. In each case the unknown mass m is
balanced by a known mass, M1 or M2, so that the rod remains horizontal. What is
the value of m in terms of the known masses?
Sqrt (M1 M2)
A system of two wheels fixed to each other is free to rotate about a frictionless
axis through the common center of the wheels and perpendicular to the page.
Four forces are exerted tangentially to the rims of the wheels, as shown above.
The magnitude of the net torque in the system about the axis is
2FR
For the wheel-and-axle system shown above, which of the following expresses
the condition required for the system to be in static equilibrium?
am1 = bm2
A cylinder rotates with constant angular acceleration about a fixed axis. The
cylinder's moment of inertia about the axis is 4 kg m^2. At time t=0 the cylinder is
at rest. At time t = 2 seconds its angular velocity is 1 radian per second.
What is the angular acceleration of the cylinder between t = 0 and t=2 seconds?
0.5 radians / s^2
A cylinder rotates with constant angular acceleration about a fixed axis. The
cylinder's moment of inertia about the axis is 4 kg m^2. At time t=0 the cylinder is
at rest. At time t = 2 seconds its angular velocity is 1 radian per second.
What is the kinetic energy of the cylinder at time t = 2 seconds?
2J
A particle is moving in a circle of radius 2 meters according to the relation theta =
3t^2 + 2t, where theta is measured in radians and t in seconds. The speed of the
particle at t = 4 seconds is
52 m/s
, A uniform stick has length L. The moment of intertidal about the center of the
stick is I (not). A particle of mass M is attached to one end of the stick. The
moment of intervals of the combined system about the center of the stick is
I + 1/4 ML^2
A light rigid rod with masses attached to its ends is pivoted about a horizontal
axis as shown above. When released from rest in a horizontal orientation, the rod
begins to rotate with an angular acceleration of magnitude
g/7l
In which of the following diagrams is the torque about point O equal in magnitude
to the torque about point X in the diagram above?
{the one with 60 degrees}
An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The
flywheel rotates clockwise on a horizontal shaft S with constant angular velocity
w. As the wheel rotates, the ant revolves past the stationary points I, II, III, IV. The
ant can adhere to the wheel with a force much greater than its own weight.
It will be most difficult for the ant to adhere to the wheel as it revolves past which
of the four points?
III
An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The
flywheel rotates clockwise on a horizontal shaft S with constant angular velocity
w. As the wheel rotates, the ant revolves past the stationary points I, II, III, IV. The
ant can adhere to the wheel with a force much greater than its own weight.
What is the magnitude of the minimum adhesion force necessary for the ant to
stay on the flywheel at point III?
mw^2r + mg (NOT mw^2r^2 + mg)
A turntable that is initially at rest is set in motion with a constant angular
acceleration a (alpha). What is the angular velocity of the turntable after it has
made one complete revolution?
Sqrt (4 pi a)
A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of
negligible mass, as shown above. The sphere-rod combination can be pivoted
about an axis that is perpendicular to the plane of the page and that passes
through one of the five lettered points. Through which point should the axis pass
for the moment of inertia of the sphere-rod combination about this axis to be the
greatest?
E
A wheel with rotational intertia I is mounted on a fixed, frictionless axle. The
angular speed of the wheel is increased from zero to wf in a time interval T.
What is the average net torque on the wheel during the time interval?
Iwf/ T
A wheel with rotational intertia I is mounted on a fixed, frictionless axle. The
angular speed of the wheel is increased from zero to wf in a time interval T.
Torque is the rotational analogue of
Force
A square piece of plywood on a horizontal tabletop is subjected to the two
horizontal forces shown above. Where should a third force of magnitude 5
newtons be applied to put the piece of plywood into equilibrium
{Down arrow in top left corner}
Diagram + A uniform rigid bar of weight W is supported in a horizontal orientation
as shown above by a rope that makes a 30 degree angle with the horizontal. The
force extorted on the bar at point O, where it is pivoted, is best represented by a
vector whose direction is which of the following?
{arrow up and to the right}
A rod of negligible mass is pivoted at a point that is off center, so that length l1 is
different from length l2. The figures above show two cases in which masses are
suspended from the ends of the rod. In each case the unknown mass m is
balanced by a known mass, M1 or M2, so that the rod remains horizontal. What is
the value of m in terms of the known masses?
Sqrt (M1 M2)
A system of two wheels fixed to each other is free to rotate about a frictionless
axis through the common center of the wheels and perpendicular to the page.
Four forces are exerted tangentially to the rims of the wheels, as shown above.
The magnitude of the net torque in the system about the axis is
2FR
For the wheel-and-axle system shown above, which of the following expresses
the condition required for the system to be in static equilibrium?
am1 = bm2
A cylinder rotates with constant angular acceleration about a fixed axis. The
cylinder's moment of inertia about the axis is 4 kg m^2. At time t=0 the cylinder is
at rest. At time t = 2 seconds its angular velocity is 1 radian per second.
What is the angular acceleration of the cylinder between t = 0 and t=2 seconds?
0.5 radians / s^2
A cylinder rotates with constant angular acceleration about a fixed axis. The
cylinder's moment of inertia about the axis is 4 kg m^2. At time t=0 the cylinder is
at rest. At time t = 2 seconds its angular velocity is 1 radian per second.
What is the kinetic energy of the cylinder at time t = 2 seconds?
2J
A particle is moving in a circle of radius 2 meters according to the relation theta =
3t^2 + 2t, where theta is measured in radians and t in seconds. The speed of the
particle at t = 4 seconds is
52 m/s
, A uniform stick has length L. The moment of intertidal about the center of the
stick is I (not). A particle of mass M is attached to one end of the stick. The
moment of intervals of the combined system about the center of the stick is
I + 1/4 ML^2
A light rigid rod with masses attached to its ends is pivoted about a horizontal
axis as shown above. When released from rest in a horizontal orientation, the rod
begins to rotate with an angular acceleration of magnitude
g/7l
In which of the following diagrams is the torque about point O equal in magnitude
to the torque about point X in the diagram above?
{the one with 60 degrees}
An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The
flywheel rotates clockwise on a horizontal shaft S with constant angular velocity
w. As the wheel rotates, the ant revolves past the stationary points I, II, III, IV. The
ant can adhere to the wheel with a force much greater than its own weight.
It will be most difficult for the ant to adhere to the wheel as it revolves past which
of the four points?
III
An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The
flywheel rotates clockwise on a horizontal shaft S with constant angular velocity
w. As the wheel rotates, the ant revolves past the stationary points I, II, III, IV. The
ant can adhere to the wheel with a force much greater than its own weight.
What is the magnitude of the minimum adhesion force necessary for the ant to
stay on the flywheel at point III?
mw^2r + mg (NOT mw^2r^2 + mg)
A turntable that is initially at rest is set in motion with a constant angular
acceleration a (alpha). What is the angular velocity of the turntable after it has
made one complete revolution?
Sqrt (4 pi a)
A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of
negligible mass, as shown above. The sphere-rod combination can be pivoted
about an axis that is perpendicular to the plane of the page and that passes
through one of the five lettered points. Through which point should the axis pass
for the moment of inertia of the sphere-rod combination about this axis to be the
greatest?
E
A wheel with rotational intertia I is mounted on a fixed, frictionless axle. The
angular speed of the wheel is increased from zero to wf in a time interval T.
What is the average net torque on the wheel during the time interval?
Iwf/ T
A wheel with rotational intertia I is mounted on a fixed, frictionless axle. The
angular speed of the wheel is increased from zero to wf in a time interval T.
