Advertisements
Advertisements
प्रश्न
A flywheel rotates with uniform angular acceleration. If its angular velocity increases from `20pi` rad/s to `40pi` rad/s in 10 seconds. Find the number of rotations in that period.
Advertisements
उत्तर
Given,
Initial angular velocity ω0 = 20 π rad/s
Final angular velocity ω = 40 π rad/s
Time t = 10 s
Solution:
Angular acceleration α = `(ω−ω_0)/t` = `(40π –20π)/10`
α = 2π rad/s2
According to the equation of motion for rotational motion
`theta = omega_0t + 1/2alphat^2 = 20pi xx 10 + 1/2 2pi xx 100 = 300pi` rad
The number of rotations = n = `theta/(2pi)`
n = `(300pi)/(2pi)` = 150 rotations.
APPEARS IN
संबंधित प्रश्न
The coefficient of static friction between a coin and a gramophone disc is 0.5. Radius of the disc is 8 cm. Initially the center of the coin is 2 cm away from the center of the disc. At what minimum frequency will it start slipping from there? By what factor will the answer change if the coin is almost at the rim? (use g = π2m/s2)
Starting from rest, an object rolls down along an incline that rises by 3 in every 5 (along with it). The object gains a speed of `sqrt 10` m/s as it travels a distance of `5/3` m along the incline. What can be the possible shape/s of the object?
Does the angle of banking depend on the mass of the vehicle?
A hollow sphere has a radius of 6.4 m. what is the minimum velocity required by a motorcyclist at the bottom to complete the circle.
A bend in a level road has a radius of 100m. find the maximum speed which a car turning this bend may have without skidding if the coefficient of friction between the tires and road is 0.8.
A bucket containing water is tied to one end of a rope 5 m long and it is rotated in a vertical circle about the other end. Find the number of rotations per minute in order that the water in the bucket may not spill.
Obtain an expression for maximum safety speed with which a vehicle can be safely driven along a curved banked road.
A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes, ______
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along, ______
What are the rotational equivalents for the physical quantities, (i) mass and (ii) force?
