## Solution Search

• January 30, 2023
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August 4, 2021
• Abhigyan Martin Ninama
September 8, 2017

## . : "Rotation and MI"

### 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…

### 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:

### 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…

### 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…

### 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…

### Rotational motion

Q- A billiard ball of mass m rolls without slipping across a table at speed v0. It collides with the lower end of a rod of mass M = 2m and length d, pivoted at its center and initially at rest in vertical position. After collision the ball rolls straight with half of its initial speed. What is the r…

### Torque

Q- (a) Calculate the force required in the deltoid muscle (Fm) to hold up the outstretched arm as shown in the figure. The mass of the arm is 2.8 kg.

(b) What is the muscle force and the reaction Fj at joint if the hand holds a ball of mass 5 kg at a distance 50 cm from the shoulder joint?

So…

### Sliding without Tipping

Q- Determine the horizontal force F necessary to slide the 100 kg crate of height 1.5 m and width 1.00 m. The crate has uniform mass distribution. The coefficient of static friction at the floor is ms = 0.4. What is the maximum height h for which with this force the crate will slide without tipping?

### Rod rotating with a particle

Q- A uniform rod AB, of mass m and length 4a, is free to rotate in a vertical plane about a fixed horizontal axis through the point X on the rod, where AX = a. The rod is hanging at rest with B below A, when it is struck at its mid point by a particle of mass 3m moving horizontally with speed u in a…

### Rotating pulley - Torque

Q- A pulley wheel of radius r and mass m is free to rotate about a fixed smooth horizontal axis through its center perpendicular to the plane of the pulley? A light in-extensible string passes over the pulley and carries particles of mass 4m and 2m, one at each end of the string. It can be assumed t…

### Rotational Motion - Reaction on axis

Q- A uniform circular disc has mass 4m and radius r. A particle of mass m is attached to the disc at point A of its circumference. The loaded disc is free to rotate about a horizontal axis which is tangential to the disc at the point B, where AB is a diameter. The disc is released from rest with AB …

### Force-Moments

Q- A timber plank 6m long and mass 50 kg is supported horizontally by two posts 1m from each end. A mass of 150 kg is placed on the plank 1m inside of the left hand supporting post. What is the force in each of the two supports?

Solution:

### Rotational Motion

Q- A uniform solid disk rolls down an inclined plane. Find the minimum coefficient of static friction that will permit the disk to roll without slipping, if the angle of the incline is 300 with the horizontal.

Solution:

### Rotational Motion

Q- A uniform rod PQ, mass m and length l is free to rotate in a vertical plane about a fixed horizontal axis passing through P. The rod is released from rest when PQ makes an angle 600 with the downward vertical. Find the magnitude of the force exerted by the rod on the pivot just after it is releas…

### Rotational Motion

Q- A rectangular signboard has a mass of 1050 kg, a height h = 1 m, and a width W = 4 m. It is held by a light rod of length 5 m that is perpendicular to a rough wall. A guy wire at 300 to the horizontal holds the sign to the wall. Note that the distance from the left edge of the sign to the wall is…

### Rotational Motion

Q- A disk of mass M1 = 350 g and radius R1 = 10 cm rotates about its symmetry axis at finitial = 157 rpm. A second disk of mass M2 = 261 g and radius R2 = 6 cm, initially not rotating, is dropped on top of the first. Frictional forces act to bring the two disks to a common rotational speed ffinal. (…

### Rotational Motion

Q- A block of mass m1 = 1 kg rests on a table with which it has a coefficient of friction 0.54. A string attached to the block passes over a pulley to a block of mass m3 = 3 kg. The pulley is a uniform disk of mass m2 = 0.4 kg and radius 15 cm. As the mass m3 falls, the string does not slip on the p…

### Rotetional Motion

Q- A uniform square lamina ABCD of mass m and side 2a is free to rotate about a horizontal axis thru A. The axis is perpendicular to the plane of lamina. The lamina is in equilibrium with C vertically below A when it is given an angular speed 2(g/a)^1/2 show that the lamina will perform complete rev…

### Moment-torque-angular Momentum

Q- A uniform stick d = 1 m long with a total mass of 750 g is pivoted at its center by means of a friction-less peg. A 5.6 g bullet is shot through the stick midway between the pivot and one end. It approaches at v0 = 409 m/s and leaves at vf = 260 m/s.

1. What is the moment of inertia of the sti…
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