Amotor produces a torque of 22 nm. it is used to accelerate a wheel of radius 10cm and moment of inertia 2 kg. m2 which is initially at rest. calculate

a)

the number of revolutions made by the wheel in the first 5s

b)

the angular velocity after 5s

c)

the acceleration of a point on the rim of the wheel after 5s

Answer

given,

torque produced, τ = 22 N.m

Radius of the wheel. r = 10 cm

Moment of inertial = 2 kg.m²

initial angular speed = 0 rad/s

time, t = 5 s

a) we know,

   τ = I α

   22 = 2 x α

    α = 11 rad/s²

  using equation of rotation motion

  θ = 137.5 rad

  θ = 137.5/2π  =  22 revolution.

b) angular velocity of the motor

c) acceleration of a point on the rim of the wheel

  radial acceleration

tangential acceleration of the point on the rim

now, acceleration of the point