Home
Class 11
PHYSICS
A wheel of mass 10 kg and radius 0.2 m i...

A wheel of mass 10 kg and radius 0.2 m is rotating at an angular speed of 100 rpm, when the motion is turned off. Neglecting the friction at the axis. Calculate the force that must be applied tangentially to the wheel to bring it to rest in 10 rev. Assumed wheel to be a disc.

Text Solution

Verified by Experts

`omega=100 rev/min`
`=5/3rev/s=(10pi)/3rad/s`
`theta=10 rev.=20pirad`
`r=0.2m`
After 10 revolutions the wheel wil come to rest by as tangential force.
Therefore the angular deceleration produced by the force
`=K=(K2)/(2K)`
therefore the torque by which the wheel will come to an rest `=IcmxxK`
`implies Fxxr=I_(cm)xx alpha`
`rarr Fxx0.2=1/2mr^2x((10pi/3)62(2xx20pi)`
`rarr F=1/2xx10xx0.2xx(10pi^2)/((9xx2xx20pi))`
`=(5pi)/18=15.7/18=0.87N`
Promotional Banner

Similar Questions

Explore conceptually related problems

A ship of mass 3xx10^(2)kg initially at rest is pulled by a force of 5xx10^(4) N through a distance of 3m. Neglecting frcition, the speed of the ship at this moment is:

A cord of negligible mass is wound round the rim of a fly wheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord as shown in Fig. 7.35. The flywheel is mounted on a horizontal axle with frictionless bearings. (a) Compute the angular acceleration of the wheel. (b) Find the work done by the pull, when 2m of the cord is unwound. (c) Find also the kinetic energy of the wheel at this point. Assume that the wheel starts from rest. (d) Compare answers to parts (b) and (c).

A fan is rotating with a speed of 450 rec/minute. Afer being switched off it comes to rest in 10s. Assuming constant angular deceleration, calculate the number of recvolutions made by it before coming to rest.

A circular racetrack of radius 300 m is banked at an angle of 20^(@) . If the coefficient of friction between the wheels of the race car and the road is 0.2, what is the approximate maximum permissible speed of the race car ?

A circular racetrack of radius 300 m is banked at an angle of 15^@ . If the coefficient of friction between the wheels of a race-car and the road is 0.2, what is the (a) optimum speed of the race- car to avoid wear and tear on its tyres, and (b) maximum permissible speed to avoid slipping ?

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres ? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable ?

A thin uniform metallic rod of length 0.5 m and radius 0.1 m rotates with an angular velocity 400rad/s is a horizontal plane about a vertical axis passing through one of its ends. Calculate (a) tenstion in the rod and (b) the elogation of te rod. The density of material of the rod is 10^(4)kg//m^(3) and the young's modulus is 2xx10^(11)N//m^(2)

On complete combustion a litre of petrol gives off heat equivalent to 3 xx 10^(7) J. In a test drive, a car weighing 1200 kg including the mass of driver, runs 15 km per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform. calculate the force of friction acting on the car during the test drive. if the efficiency of the car engine were 0.5.