Advertisements
Advertisements
Question
Define angular velocity.
Advertisements
Solution
Angular velocity of a particle is the rate of change of angular displacement.
APPEARS IN
RELATED QUESTIONS
In U. C. M (Uniform Circular Motion), prove the relation `vec v = vec w xx vec r`, where symbols have their usual meanings.
Draw a neat labelled diagram of conical pendulum. State the expression for its periodic time in terms of length.
Read the statement below carefully and state, with reason, if it is true or false:
The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.
A particle starts from the origin at t = 0 s with a velocity of 10.0 `hatj "m/s"` and moves in the x-y plane with a constant acceleration of `(8.0 hati + 2.0 hatj) ms^(-2)`.
- At what time is the x-coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?
- What is the speed of the particle at the time?
Is it possible to have an accelerated motion with a constant speed? Explain
Why is the motion of a body moving with a constant speed around a circular path said to be accelerated?
Earth moves around the sun with uniform velocity.
A uniform linear motion is unaccelerated, while a uniform circular motion is an accelerated motion.
Answer the following question.
Show that the centripetal force on a particle undergoing uniform circular motion is -mrω2.
Solve the following problem.
A car moves in a circle at a constant speed of 50 m/s and completes one revolution in 40 s. Determine the magnitude of the acceleration of the car.
Solve the following problem.
A projectile is thrown at an angle of 30° to the horizontal. What should be the range of initial velocity (u) so that its range will be between 40m and 50 m? Assume g = 10 m s-2.
The angle subtended by the vector A = `5hat"i" + 3hat"j" + 12hat"k"` with the X-axis is ______.
A uniform rod of length '6L' and mass '8 m' is pivoted at its centre 'C'. Two masses 'm' and ' 2m' with speed 2v, v as shown strikes the rod and stick to the rod. Initially the rod is at rest. Due to impact, if it rotates with angular velocity 'w1' then 'w' will be ________.

The ratio of the angular speed of minute hand and hour hand of a watch is ____________.
A particle performs uniform circular motion in a horizontal plane. The radius of the circle is 8 cm. The centripetal force acting on the particle is 15 N. Its kinetic energy is ____________.
A disc has mass 'M' and radius 'R'. How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity 'ω' in time t?
A wheel is 0.25 m in radius. When it makes 15 revolutions per minute, its linear speed at the point on circumference is ____________.
In uniform motion, an object travels equal ______ in ______ interval of time.
The motion of the bus is ______ motion.
For a particle performing uniform circular motion, choose the correct statement(s) from the following:
- Magnitude of particle velocity (speed) remains constant.
- Particle velocity remains directed perpendicular to radius vector.
- Direction of acceleration keeps changing as particle moves.
- Angular momentum is constant in magnitude but direction keeps changing.
A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off the angular velocity becomes `(1/4)^"th"` of the original in time 't' and 'n' revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are ______. (Angular retardation is uniform)
A particle moves along a circle of radius r with constant tangential acceleration. If the velocity of the particle is v at the end of second revolution, after the revolution has started, then the tangential acceleration is ______.
The acceleration of a point on the rim of a flywheel 1 m in diameter, if it makes 1200 rpm is ______.
A wheel is Subjected to uniform angular acceleration about its axis. Initially. its angular velocity is zero. In the first 2 s, it rotates through an angle θ1, in the next 2 s, it rotates through an angle θ2. The ratio of `theta_2/theta_1` is ______.
The kinetic energy K of a particle moving along a circle of radius R depends on the distance covered s as K = as2, where a is a constant. The force acting on the particle is ______.
Explain the meaning of uniform circular motion.
Why is uniform circular motion said to be accelerated?
What is the direction of the velocity of an object at any point during uniform circular motion?
The relationship between an object's linear velocity (v) and its angular velocity (ω) in a circular path of radius (r) is given by:
What is the direction of the velocity of an object at any point during uniform circular motion?
