Advertisements
Advertisements
Question
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?
Advertisements
Solution
Length of the string, l = 80 cm = 0.8 m
Number of revolutions = 14
Time taken = 25 s
Frequency v = `"Number of revolution"/"Time taken" = 14/25 Hz`
Angular frequency, ω = 2πν
`2xx22/7xx14/25 = 88/25 rads^(-1)`
Centripetal acceleration, `a_c = omega^2 r`
=`(88/25)^2 xx 0.8`
= `0.80 xx 88/25 xx 88/25`
= 9.90 `ms^(-2)`
The direction of centripetal acceleration is always directed along the string, toward the centre, at all points.
APPEARS IN
RELATED QUESTIONS
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? Name such type of motion.
| A small pebble tied at one end of a string is placed near the periphery of a circular disc, at the centre of which the other end of the string is tied to a peg. The disc is rotating about an axis passing through its centre. |
- What will be your observation when you are standing outside the disc? Explain.
- What will be your observation when you are standing at the centre of the disc? Explain.
State True or False
The earth moves around the sun with a uniform.
The motion of the moon around the earth in a circular path is an accelerated motion.
Solve the following problem.
A particle moves in a circle with a constant speed of 15 m/s. The radius of the circle is 2 m. Determine the centripetal acceleration of the particle.
Is the uniform circular motion accelerated? Give reasons for your answer.
What is meant by uniform circular motion? Give two examples of uniform circular motion.
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 ________.
A particle goes round a circular path with uniform speed v. After describing half the circle, what is the change in its centripetal acceleration?
A small sphere is attached to a cord and rotates in a vertical circle about a point O. If the average speed of the sphere is increased, the cord is most likely to break at the orientation when the mass is at ____________.
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 particle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum, the radial force acting on the particle is ______.
Certain neutron stars are believed to be rotating at about 1 rev/s. If such a star has a radius of 1.6 km, the acceleration of an object on the equator of the star will be nearly ____________.
Select the WRONG statement.
A cyclist is riding with a speed of 43.2 km/h. As he approaches a circular turn on the road of radius 60 m, he applies brakes and reduces his speed at constant rate of 1.8 ms-2. The magnitude of the net acceleration of the cyclist is ______.
If a body is moving in a circle of radius r with a constant speed v, its angular velocity is ______.
A horizontal circular platform of mass M is rotating at angular velocity ω about a vertical axis passing through its centre. A boy of mass m is standing at the edge of the platform. If the boy comes to the centre of the platform, then the new angular velocity becomes ______.
The acceleration of a point on the rim of a flywheel 1 m in diameter, if it makes 1200 rpm is ______.
Explain the meaning of uniform circular motion.
