Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Answer in brief:
Why are curved roads banked?
Answer in Brief:
A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and a radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the center. Calculate x if the wheel now rotates at 80 rpm.
A big dumb-bell is prepared by using a uniform rod of mass 60 g and length 20 cm. Two identical solid spheres of mass 25 g and radius 10 cm each are at the two ends of the rod. Calculate the moment of inertia of the dumb-bell when rotated about an axis passing through its centre and perpendicular to the length.
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 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.
A body weighing 0.5 kg tied to a string is projected with a velocity of 10 m/s. The body starts whirling in a vertical circle. If the radius of the circle is 0.8 m, find the tension in the string when the body is at the top of the circle.
Derive an expression for the kinetic energy of a rotating body with uniform angular velocity.
What is a conical pendulum? Obtain an expression for its time period
Obtain an expression for maximum safety speed with which a vehicle can be safely driven along a curved banked road.
What is the difference between rotation and revolution?
