A girl of mass M stands on the rim of a frictionless merry-go-round of radius R and rotational inertia I that is not moving. She throws a rock of mass m horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground, is v. Afterward, what are (a) the angular speed of the merry-go-round and (b) the linear speed of the girl?
Mass of girl is M
Merry go round of radius is R
Rotational inertia is I
Using the formula and , find the angular speed of the merry-go-round and the linear speed of the girl.
Formulae are as follow:
Where, is angular frequency, L is angular momentum, I is moment of inertia, v is velocity and R is radius.
Initially, the merry-go-round is not moving; therefore the initial angular momentum of the system is zero.
The final angular momentum the girl and merry-go-round is,
The final angular momentum associated with the thrown rock is .
Therefore, according to the conservation of the angular momentum,
Hence, the angular speed of the merry-go-round is .
The linear speed of the girl is,
Hence, the linear speed of the girl is .
Therefore, using the formula for the angular momentum and relationship between linear and angular velocity, the expression for linear and angular velocity can be found.
A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on a mass less axle through its center (Fig. 11-62). The radius of the axle is 0.200 m, and the rotational inertia of the wheel–axle combination about its central axis is 0.600 kg.m2. The wheel is initially at rest at the top of a surface that is inclined at angle . with the horizontal; the axle rests on the surface while the wheel extends into a groove in the surface without touching the surface. Once released, the axle rolls down along the surface smoothly and without slipping. When the wheel–axle combination has moved down the surface by 2.00 m, what are (a) its rotational kinetic energy and (b) its translational kinetic energy?
Question: At time t, the vector gives the position of a3 .0 kg particle relative to the origin of an coordinate system ( is in meters and t is in seconds). (a) Find an expression for the torque acting on the particle relative to the origin. (b) Is the magnitude of the particle’s angular momentum relative to the origin increasing, decreasing, or unchanging?
In Figure a bullet is fired into a block attached to the end of a non uniform rod of mass The block–rod–bullet system then rotates in the plane of the figure, about a fixed axis at A. The rotational inertia of the rod alone about that axis at A is Treat the block as a particle.
(a) What then is the rotational inertia of the block–rod–bullet system about point A?
(b) If the angular speed of the system about A just after impact what is the bullet’s speed just before impact?
In 1980, over San Francisco Bay, a large yo-yo was released from a crane. The 116kg yo-yo consisted of two uniform disks of radius 32cm connected by an axle of radius 3.2cm (a) What was the magnitude of the acceleration of the yo-yo during its fall ? (b) What was the magnitude of the acceleration of the yo-yo during its rise? (c) What was the tension in the cord on which it rolled? (d) Was that tension near the cord’s limit of 52kN? Suppose you build a scaled-up version of the yo-yo (same shape and materials but larger). (e) Will the magnitude of your yo-yo’s acceleration as it falls be greater than, less than, or the same as that of the San Francisco yo-yo? (f) How about the tension in the cord?
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