Exam 10: Rotation

A uniform solid cylinder made of lead has the same mass and the same length as a uniform solid cylinder made of wood. The rotational inertia of the lead cylinder compared to the wooden one is:

$\tau$ = I $\alpha$ for an object rotating about a fixed axis, where $\tau$ is the net torque acting on it, I is its rotational inertia, and $\alpha$ is its angular acceleration. This expression:

A disk starts from rest and rotates about a fixed axis, subject to a constant net torque. The work done by the torque during the second revolution is ______ as the work done during the first revolution.

The angular velocity of a rotating turntable is given in rad/s by ω(t) = 4.5 + 0.64t - 2.7t². What is its angular acceleration at t = 2.0 s?

A small disk of radius R₁ is fastened coaxially to a larger disk of radius R₂. The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead view below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force as shown. The tension in the string pulling the block is:

A and B are two solid cylinders made of aluminum. Their dimensions are shown. The ratio of the rotational inertia of B to that of A about the common axis X─X' is:

A wheel starts from rest and has an angular acceleration that is given by $\alpha$ (t) = 6 rad/s⁴)t^2. The angle through which it turns in time t is given by:

If a wheel is turning at 3.0 rad/s, the time it takes to complete one revolution is about:

The rotational inertia of a thin cylindrical shell of mass M, radius R, and length L about its central axis (X - X') is:

A torque of 170 N∙m does 4700 J of work on a rotating flywheel. If the flywheel's initial kinetic energy is 1500 J, what is its final kinetic energy?

One revolution per minute is about:

Instantaneous angular speed is:

If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:

A thin rod of length L has a density that increases along its length, ρ = ρ₀x. What is the rotational inertia of the rod around its less dense end?

One-dimensional linear position is measured along a line, from a point designated x = 0. One-dimensional angular position:

A torque of 470 N∙m acts on a flywheel. At the instant that the flywheel's angular speed is 56 rad/s, at what rate is work being done by the torque?

A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applied. Of the following alternatives the greatest angular acceleration is obtained if the force is:

A constant torque of 260 N∙m acts on a flywheel. If the flywheel makes 25 complete revolutions in 2 minutes, what is the power exerted by the torque?

A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s⁴)t^2. It stops in a time of:

The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point P is: