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. : "Rotation and MI"

Rotational Motion

Q- A solid wheel of mass 30 kg is rolled toward the left along a horizontal surface under the action of a horizontal force of magnitude 200 N, acting at the center of the wheel . If the friction is sufficient to prevent slipping, what is the magnitude of linear acceleration of the center of the whee…

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Rotation: Sphere over Sphere

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…

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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…

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Rotational Motion

Q- A solid ball with mass M and radius R is rolling without slipping on a flat surface at 10 m/s. It then gets a small slope and rolls down 2 m from the top. Find the velocity of the ball after it passes the slope.

Solution:

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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.

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Rotational Oscillations

Q- Two disks with moments of inertia I1 (top disk) and I2 (bottom disk) are connected by a mass-less torsion spring which produces a restoring torque with magnitude |τ| =  c |θ12| on each disk, where θ1 and θ2 are the angular positions of the disks. (You can imagine that this system is free…

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Rotational Motion

Q- A torque of 50 N.m accelerates a wheel from rest to 100 rev/min in 5 seconds.

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

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

(c) What is the moment of inertia of the wheel?

Solution:

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Rotational Motion

Q- Two blocks of mass m1 = 4 kg and m2 = 3 kg are attached to the ends of a string that passes over a pulley of mass M = 2 kg and radius 20 cm. Find angular acceleration of the pulley considering it as a uniform disk.

Solution:

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Rotational Motion

Q- A torque of 50 N.m accelerates a wheel from rest to 100 rev/min in 5 seconds.

(a) What is the angular displacement of the wheel in 5 second?

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

(c) What is the moment of inertia of the wheel?

Solution:

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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?

Solution:

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Rotational Motion: Angular Momentum

Q- A disk of mass M = 400 grams and radius R = 30 cm is free to rotate about its horizontal axis. A lump of clay of mass m = 100 grams falls from height h = 2m and sticks to the disk at the farthest point from the center. Find the angular velocity of the disk after collision.

Solution:

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Rotational Motion

Q- A ball is rolling without sliding up an incline with a velocity of 7 m/s. What will be its velocity when it reaches a vertical height h = 2 m above its initial position? 

Solution:

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Rotational Motion

Q- A steel shaft (density = 8050 kg/m3) is 2m long and is accelerated from rest to 400 rpm in 6 seconds by a torque of 100 Nm. Determine the diameter of the shaft.

Solution:

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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…

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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…

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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-m2, which is free to rotate about its horizontal axis. The cable is horizontal between the pull…

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Rotational Motion

Q- A wad of sticky clay with mass m and velocity vi 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…

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Rotational Motion: Angular Momentum

Q- Big ben the parliament tower clock in London, has hour and minute hands with lengths of 2.70 m and 4.50 m and masses of 60.0 kg and 100 kg respectively. Calculate the total angular momentum of these hands about the center point. Treat the hands as long thin uniform rods.

Solution:

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Rotational Motion

Q- A top has a moment of inertia equal to 4.00 x 10-4 kg.m2 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…

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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 103 kg/m3, find its moment of inertia about an ax…

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