Q- A solid sphere of radius R starts at rest on top of a semicircular track of radius S., as shown in the figure. The sphere rolls *without slipping *along the track until it falls off the track at point B. Point A is a vertical distance H above the ground; the height of point B is unknown. You may as…

## . : "Rotation and MI"

### Rotation: Sphere over Sphere

### Rotational Motion

Q- A solid disk of mass M = 1.3 kg and radius R = 25 cm is free to rotate in a vertical plane about a horizontal axis going through its center. The disk is originally at rest. A piece of clay of mass m= 200 gm (consider particle) drops from 2.5 m above the center of the disk and sticks to its edge a…

### Rotation: Torque

Q- A block of weight 150 lb is placed on a rough horizontal surface and a horizontal force P = 60 lb is acting on it as in figure. The friction is sufficient to prevent sliding. Find the horizontal distance between the line of action of the weight of the block and the normal reaction of the surface.

### Rotational Oscillations

Q- Two disks with moments of inertia I_{1} (top disk) and I_{2} (bottom disk) are connected by a mass-less torsion spring which produces a restoring torque with magnitude |τ| = c |θ_{1}-θ_{2}| on each disk, where θ_{1} and θ_{2} are the angular positions of the disks. (You can imagine that this system is free…

### Rotational Motion

Q- A wheel starting from rest with uniform angular acceleration makes 3 revolutions in 8 s

(a) What is the angular acceleration of the wheel?

(b) What is its angular velocity at t = 8 s?

(c) What is the linear speed of a particle at distance 0.50 m from the axis of rotation at t = 8 s?

### Torque, Lever

Q- A fulcrum is created by balancing a ruler on a pencil in the middle. Six one rupee coins are placed at 10 cm to the left of the pivot point.

(a) what is the torque exerted by the stack of the six coins about the pivot point if each coin has a mass of 10 grams?

(b) if the ruler is to be balanced…

### Rotational Motion

Q- A light cylindrical axle of radius r is free to rotate about its vertical axis. The upper end of the axle is attached to a light horizontal cross bar with two small masses, each M, at a distance R from the axle. A light string is wrapped on the axle and its free end is passing over a smooth light…

### Rotational Motion

Q- A light cable is used to pull a block of mass 10 kg on a rough horizontal surface (coefficient of friction 0.2). The cable is passed through a fixed pulley of radius 0.25 m and moment of inertia 1.2 kg-m^{2}, which is free to rotate about its horizontal axis. The cable is horizontal between the pull…

### Rotational Motion

Q- A wad of sticky clay with mass m and velocity v_{i} is fired at a solid cylinder of mass M and radius R. The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a distan…

### Rotational Motion

Q- A top has a moment of inertia equal to 4.00 x 10^{-4} kg.m^{2} and is initially at rest. It is free to rotate about the stationary vertical axis AA'. A string wrapped around a peg along the axis of the top, is pulled in such a manner as to maintain a constant tension of 5.57 N. If the string does not s…

### Rotational Motion: Moment of Inertia

Q- A car tire of inner radius 16.5 cm and outer radius 30.5cm is modeled as having two sidewalls of uniform thickness 0.635cm and a tread wall of uniform thickness 2.50cm and width 20.0cm over it. Assume the rubber has uniform density equal to 1.10 x 10^{3} kg/m^{3}, find its moment of inertia about an ax…

### Rotational motion

Q- A globe of mass M and radius R can rotate about its fixed vertical axis. A block of mass m is attached by a massless string/pulley system as shown. As the block is released, it causes the globe to spin. If the block starts at rest, at what speed does the block hit the ground after it falls a dis…

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