Exam 7: Rotational Motion

A solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane.If the angular velocity of the disk is 4.27 rad/s at the bottom,what is the height of the inclined plane?

A particular motor can provide a maximum of 110.0 N · m of torque.Assuming that all of this torque is used to accelerate a solid,uniform flywheel of mass 10.0 kg and radius 3.00 m,how long will it take for the flywheel to accelerate from rest to 6.04 rad/s?

A machinist turns the power on to a grinding wheel,at rest,at time t = 0 s.The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 29 rad/s.The wheel is run at that angular velocity for 27 s and then power is shut off.The wheel slows down uniformly at 2.7 rad/s² until the wheel stops.In this situation,the average angular velocity in the time interval from t = 0 s to t = 25 s is closest to:

-In the figure,a mass of 35.30 kg is attached to a light string that is wrapped around a cylindrical spool of radius 10 cm and moment of inertia 4.00 kg · m2.The spool is suspended from the ceiling,and the mass is then released from rest a distance 3.50 m above the floor.How long does it take to reach the floor?

A tall tree and a short tree (both having the same width and mass density)are cut at the base at the same time,and begin tipping over.Which tree hits the ground first?

-In the figure are scale drawings of four objects,each of the same mass and uniform thickness.Which has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing? In each case the axis passes through point P.

-A light triangular plate OAB is in a horizontal plane.Three forces,F₁ = 2 N,F₂ = 4 N,and F₃ = 7 N,act on the plate,which is pivoted about a vertical axis through point O.In the figure,consider the counterclockwise sense as positive.The sum of the torques about the vertical axis through point O,acting on the plate due to forces F₁,F₂,and F₃,is closest to:

A solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane.If the angular velocity of the disk is 5.35 rad/s at the bottom,what is the height of the inclined plane?

A potter's wheel (a solid,uniform disk)of mass 7.0 kg and radius 0.65 m spins about its central axis.A 2.1 kg lump of clay is dropped onto the wheel at a distance 0.41 m from the axis.Calculate the rotational inertia of the system.

If two objects have the same moment of inertia,they must have the same mass.

An electrical motor spins at a constant 2695.0 rpm.If the armature radius is 7.165 cm,what is the acceleration of the edge of the rotor?

A rectangular sign h = 20.0 cm high and w = 11.0 cm wide loses three of its four support bolts and rotates into the position as shown,with P₁ directly over P₃.It is supported by P₂,which is so tight it holds the sign from further rotation.Find the gravitational torque about P₂,if the mass of the sign is 5.0 kg.

A force in the +y direction applied at the point x = 2.3 m,y = 1.4 m gives rise to a torque of 71 N · m about the origin.Find the magnitude of the force.

A machinist turns the power on to a grinding wheel,at rest,at time t = 0 s.The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 38 rad/s.The wheel is run at that angular velocity for 30 s and then power is shut off.The wheel slows down uniformly at 2.1 rad/s² until the wheel stops.In this situation,the angular acceleration of the wheel between t = 0 s and t = 10 s is closest to:

A tire is rolling along a road,without slipping,with a velocity v.A piece of tape is attached to the tire.When the tape is opposite the road (at the top of the tire),it's velocity with respect to the road is

A 0.18 m radius pulley is free to rotate about a horizontal axis.A 4.2 kg mass and a 8.0 kg mass are attached by a massless string,which is hung over the pulley.If the string does not slip,calculate the magnitude of the net torque on the pulley about its rotational axis.

-The table shows the masses and the coordinates x and y of a set of three point masses in the x-y plane.The masses are interconnected by light struts,forming a rigid body.The moment of inertia of the rigid body,through the center of mass and perpendicular to the x-y plane,is closest to: