Question

A flat uniform circular disk (radius = 3.00 m, mass = 1.00 ✕ 102 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 50.0 kg person, standing 1.75 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 2.60 m/s relative to the ground. Find the resulting angular speed of the disk (in rad/s) and describe the direction of the rotation.

Answer #1

A flat uniform circular disk (radius = 5.44 m, mass = 320 kg) is
initially stationary. The disk is free to rotate in the horizontal
plane about a frictionless axis perpendicular to the center of the
disk. A 66.4-kg person, standing 2.40 m from the axis, begins to
run on the disk in a circular path and has a tangential speed of
2.97 m/s relative to the ground. Find the magnitude of the
resulting angular speed (in rad/s) of the...

A uniform disk of radius 0.529 m and unknown mass is constrained
to rotate about a perpendicular axis through its center. A ring
with same mass as the disk\'s is attached around the disk\'s rim. A
tangential force of 0.223 N applied at the rim causes an angular
acceleration of 0.103 rad/s2. Find the mass of the disk.

A disk with mass m = 10.3 kg and radius R = 0.34 m begins at
rest and accelerates uniformly for t = 16.8 s, to a final angular
speed of ω = 26 rad/s.
1)
What is the angular acceleration of the disk?
rad/s2
2)
What is the angular displacement over the 16.8 s?
rad
3)
What is the moment of inertia of the disk?
kg-m2
4)
What is the change in rotational energy of the disk?
J
5)...

A uniform
circular platform of mass 100 kg and radius 3.0 m is mounted on a
frictionless vertical axle and is initially stationary. A girl of
mass 40 kg stands on the rim of the platform. She begins to walk
along the rim at a speed of 1.5 m/s relative to the ground in
clockwise direction. What is the resulting angular velocity of the
platform.

A thin uniform rod has a length of 0.490 m and is rotating in a
circle on a frictionless table. The axis of rotation is
perpendicular to the length of the rod at one end and is
stationary. The rod has an angular velocity of 0.37 rad/s and a
moment of inertia about the axis of 3.50×10−3 kg⋅m2 . A
bug initially standing on the rod at the axis of rotation decides
to crawl out to the other end of...

A wheel (disk) of radius 0.2 m and mass 1 kg are mounted on a
frictionless horizontal axis. A massless cord is wrapped around the
wheel and attached to a 2 kg object that slides on a frictionless
surface inclined at an angle of 60 degrees with the horizontal.
What is the acceleration of the block as well as the angular
acceleration of the wheel about its axis of rotation?
Answer: 6.93 m/s^2, 34.64 rad/s^2

A thin uniform rod has a length of 0.430 m and is rotating in a
circle on a frictionless table. The axis of rotation is
perpendicular to the length of the rod at one end and is
stationary. The rod has an angular velocity of 0.32 rad/s and a
moment of inertia about the axis of 3.20×10−3 kg⋅m2 . A bug
initially standing on the rod at the axis of rotation decides to
crawl out to the other end of...

A disk with mass m = 8.5 kg and radius R = 0.35 m begins at rest
and accelerates uniformly for t = 18.9 s, to a final angular speed
of ? = 29 rad/s.
a) What is the angular acceleration of the disk?
b) What is the angular displacement over the 18.9 s?
c) What is the moment of inertia of the disk?
d) What is the change in rotational energy of the disk?
e) What is the tangential...

QUESTION 27
A uniform disk of radius 0.40 m and mass 31.0 kg rolls on a
plane without slipping with angular speed 3.0 rad/s. The rotational
kinetic energy of the disk is __________. The moment of inertia of
the disk is given by 0.5MR2.

A cockroach of mass m lies on the rim of a uniform disk of mass
3.00 m that can rotate freely about its center like a
merry-go-round. Initially the cockroach and disk rotate together
with an angular velocity of 0.466 rad/s. Then the cockroach walks
halfway to the center of the disk. (a) What then is the angular
velocity of the cockroach-disk system? (b) What is the ratio K/K0
of the new kinetic energy of the system to its initial...

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