Is rotation is also a type of motion?

In this video we will discuss about angular variable, angular position and angular displacement and angular distance.

A pendulum is oscillating in vertical plane such that the time taken from one extreme position to the other is 1 sec. The angle made by the pendulum at extreme position is 30^{ 0 } . If the pendulum starts from the left extreme position. Find the angular displacement and distance of the pendulum after

a) 1 sec

b) 3 sec

In this we will discuss the meaning of angular velocity and angular acceleration and how to find its direction.

Two particles move in concentric circles of radius r_{ 1} and r_{ 2 } such that they maintain a straight line with center.

The ratio of their angular velocities is

An object follows a curved path. The following quantities may remain constant during the motion.

(a) speed

(b) velocity

(c) acceleration

(d) magnitude of acceleration

Statement 1: A body with constant acceleration always moves along a straight line.

Statement 2: A body with constant magnitude of acceleration may not speed up.

In this video we will give the formulation of angular motion relating with the translational motion equation.

In this video we will discuss about the relation between the translational and rotational variables like angular speed and translational speed, angular acceleration and translational acceleration.

In this video we will discuss about the centripetal acceleration value for the case when the angular speed is constant or for uniform circular motion.

In this video we will discuss what do we mean by non uniform circular motion. And finding the net acceleration of the object by knowing the meaning of tangential acceleration as well.

In this video we will discuss what do we mean by centripetal force and is that a new force? and the value of centripetal force.

Three identical cars A, B and C are moving at the same speed on three bridges. The car A goes on a plane bridge, B on a bridge convex upward and C goes on a bridge concave upward. Let FA, FB and FC be the normal forces exerted on the cars by the bridge when they are at the middle of bridges.

a) FA is maximum of the three forces

b) FB is maximum of the three forces

c) FC is maximum of the three forces

d) FA = FB = FC

In this video we will discuss about a new pseudo force known as centrifugal force. Is centripetal and centrifugal force form action reaction?

What do we mean by the radius of curvature? Can we break the curved path into circular path?

And how to find the value of radius of curvature. Is it necessary that the object should move in a curved path to have angular velocity?

A projectile is launched at speed vo making an angle q with the horizontal.

Find the

a) Radius of curvature at

i) Highest point

ii) same horizontal height.

b) Angular velocity w.r.t. point of projection at

i) Highest point

ii) same horizontal height. ( Given R = 2H )

Two particles are fired at angle q and (90 - q) to the horizontal with the same speed vo. The ratio of their radii at the highest points is

(a) cos^{2} q

(b) tan^{2} q : 1

(c) 1 : 1

(d) cot^{2} q : 1

A ball of mass 1 kg is attached to a light string of length 4m. The ball is whirled on a horizontal smooth surface in a circle of radius 4m as shown in Fig. If the string can withstand tension up to 100 N, what is the maximum speed at which the ball can be whirled.

A particle of mass m is suspended from a string of length L. The particle revolves with constant speed v in a horizontal circle. The string sweeps out the surface of a cone of semi vertex angle q. The system shown is commonly known as a conical pendulum. Find an expression for v in terms of L, g and q.

A puck of mass m slides in a circle of radius r on a frictionless table while attached to a hanging cylinder of mass M by a cord through a hole in the table. What speed keeps the cylinder at rest?

A 1.34 kg ball is connected by means of two massless strings, each of length

L = 1.70 m, to a vertical, rotating rod. The strings are tied to the rod with separation d = 1.70 m and are taut. The tension in the upper string is 35 N.

What are the

A car moves on a horizontal track of radius r and the coefficient of friction between road and tires of the car is m.

a) Find the maximum speed of the car if it given that car moves with constant velocity

b) If the speed of the car is increasing constantly at rate dv/dt = a. Find the speed at which car will skid.

Figure depicts an overhead view of a cars path as the car travels toward a wall. Assume that the driver begins to apply brakes when the distance from the wall is d = 107 m, and mass of the car m = 1,400 kg, its initial speed as v^{0} = 35 m/s, and the coefficient of static and kinetic friction between the tires and the road is 0.50 and 0.40 respectively. Assume that the cars weight is distributed evenly on the four wheels, even during braking.

To avoid the crash, should the driver apply brakes and stop before the wall or elect to turn the car so that it barely misses the wall.

Figure represents a car of mass m as it moves at a constant speed v of 20 m/s around a banked circular track of radius R = 200 m.

a) If the frictional force from the track is negligible, what bank angle q prevents sliding?

b) If ms = 0.1 find the range of speeds for which the car doesn?t slip?

A person of mass m is standing in a cylindrical roller of radius R = 2.1 m. The co-efficient of static friction between the person and rollers wall is ms = 0.40 When the roller is rotated, the person also rotates with the roller and is pinned to the wall of the roller. What minimum speed v must the cylinder have if the person is not to fall ?

A block of mass m slides from a point A as shown in the figure. Assuming that the loop is a circle of radius R = 2.7 m.

What is the least speed v at top of the loop (C) to remain in contact with it there?

A small ball of mass m is attached to a string of length R and moves in a vertical circle with a speed v m/s about a fixed point O as illustrated. Find the tension in the string, when it makes an angle q with the vertical, in terms of v, q and g.

A small ball of mass m is attached to a string of length R and moves in a vertical circle with a speed v m/s about a fixed point O as illustrated. Find the tension in the string, when it makes an angle q with the vertical, in terms of v, q and g.

The smooth block B, having mass M, is attached to the vertex A of the right circular cone using a light cord. The cone is rotating at a constant angular rate about the Z axis such that the block attains speed v (Figure). At this speed, determine the tension in the cord and the reaction which the cone exerts on the block. neglect the size of the block.

Given:

M = 0.2 kg

b = 400mm

v = 0.5m/s

c = 200mm

a = 300mm

g = 9.81 m/s^{ 2 }

A man has mass M and sits at a distance d from the center of a rotating platform (Figure). Due to the rotation his speed is increased from rest by the rate v. If the coefficient of static friction between his clothes and the plateform is ms, determine the time required to cause him to slip.

Given:

M = 80 kg

ms = 0.3

d = 3m

v = 0.4 m/s^{ 2}

g = 9.81 m/s^{2 }

The two balls of mass mA = 10 kg and mB = 15 kg are connected by an elastic string and supported on a turntable as shown in figure. When the turntable is at rest, the tension in the string is T = 100 N and the balls exert this same force on each of the stops. What forces will they exert on the stops when the turntable is rotating uniformly about vertical axis OO at 60 rpm?

Block A has a mass of mA = 15 kg and B has mass of mB = 45 kg. They are on a rotating surface and connected by a string as shown in figure. Determine the value of w at which radial sliding will occur. The coefficient of friction between blocks and the surface is 0.25.

A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity in a circular path of radius R. A smooth groove AB of length L << R is made on the surface of the table. The groove makes an angle q with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move along AB. Find the time taken by the particle to reach the point B.

A table with smooth horizontal surface is fixed in a cabin which moves in a circle of a large radius R. A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on the table are connected through a string going over the pulley. Initially the masses are held by a person with the string along the outward radius and then the system is released from rest (with respect to the cabin). Find the magnitude of the initial acceleration of the masses as seen from the cabin and the tension in the string.

A uniform metal ring of mass m and radius R is placed on a smooth horizontal table and is set rotating about its own axis with a speed of v. Find the tension in the ring.

A chain of mass m, radius r (mass uniformly distributed) is kept on a cone with semi-vetex angle q. The chain moves by an angular velocity w.Find the tension in the chain due to rotation.

An elastic cord having an unstreched length L, stiffness K, and mass per unit length l is stretched around the drum of radius t (2p > L). Determine the angular velocity of the cord due to the rotation of the drum, which will allow the cord to loosen its contact with the drum.

The pendulum bob B of mass M is released from rest when q = 0.

Determine the initial tension in the cord and also at the instant the bob reaches point D, q = q1. Neglect the size of the bob.

Given :

M = 3 Kg

q1 = 45 deg

L = 2 m

g = 9.81 m/s2

A ball suspended by a thread swings in a vertical plane so that its acceleration values in the extreme and the lowest position are equal. Find the thread deflection angle in the extreme position.

The angular acceleration of the toppling pole is given by a = k sin q, where q is the angle between the axis of the pole and the vertical, and k is a constant. The pole starts from rest at q = 0. The length of the pole is L. Find

a) the tangential and

b) the centripetal acceleration of the upper end of the pole in terms of k, q and L.

The small body A starts sliding off the top of smooth sphere of radius R. Find the angle q corresponding to the point at which the body breaks off the sphere, as well as the break-off velocity of the body.

A cyclist rides along the circumferences of a circular horizontal plane of radius R, the friction coefficient being dependent only on distance r from the centre O of the plane as m = m0 (1- r / R), where m0 is a constant. Find the radius of the circle with the centre at the point along which the cyclist can ride with the maximum velocity. What is this velocity?

A car moves uniformly along a horizontal sine curve y = a sin (x/ ), where a, and are certain constants. The coefficient of friction between the wheels and the road is equal to k.

At what max velocity can the car ride without sliding?

A table with smooth horizontal surface is turning at an angular speed w about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance a from the centre.

a) Find the speed of the particle w.r.t groove as its distance from the center becomes L.

b) Find normal contact force by the side walls of the groove.

A block of mass m is given a velocity vo at t = 0 inside a circular plate as shown in the figure. The horizontal part of the plate is frictionless but the wall of the plate is rough. The coefficient of friction between the wall of the plate and the block is m. Find the

a) velocity as a function of t and

b) velocity as a function of q.

A collar having a mass M and negligible size slides over the surface of a horizontal circular rod for which the coefficient of kinetic friction is.If the collar is given a speed vI and then released at q = 0 deg, determine how far it slides on the rod before coming to rest.

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