A roller in a printing press turns through an angle `theta=3t^(2)-t^(3) rad`. (a) Calculate the angular velocity and angular acceleration as a function of time `t`. (b) What is the maximum positive angular velocity and at what time `t` does it occur?

A roller in a printing press turns through an angle `theta=3t^(2)-t^(3

1.	A roller in a printing press turns through an angle `theta=3t^(2)-t^(3) rad`. (a) Calculate the angular velocity and angular acceleration as a function of time `t`. (b) What is the maximum positive angular velocity and at what time `t` does it occur?
Answer» (a) `theta=3t^(2)-t^(3)` `omega=(d theta)/(dt)=6t-3t^(2)` `alpha=(domega)/(dt)=6-6t` (b) `omega` is maximum when `alpha=(domega)/(dt)=0` `6-6t = 0 implies t = 1 s` `omega_(max)=6(1)-3(1)^(2)= 3 rad//s`

Discussion

No Comment Found

Related InterviewSolutions

A solid cylinder and a sphere, having the same mass, rolls without slipping with the same linear velocity. If the kinetic energy of the cylinder is `75 J`, that of the sphere must beA. `60 J`B. `70 J`C. `80 J`D. `90 J`
The M.I. of solid sphere of mass M and radius R about its diameter isA. `(2)/(5) MR^(2)`B. `(7)/(5)MR^(2)`C. `(2)/(3)MR^(2)`D. `(5)/(3)MR^(2)`
If a solid sphere of mass 500 gram rolls without slipping with a velocity of 20 cm/s, then the rolling kinetic energy of the sphere will beA. 140 JB. 280 JC. 0.014 JD. 0.028 J
If I is the M.I. of a solid sphere about an axis parallel to a diameter of the sphere and at a distance x from it, which of following graphs represents the variation of I with xA. B. C. D.
A disc is rotaing with an angular velocity `omega_(0)`. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes `(omega_(0))/(2)` after n rotations. How many more rotations will it make before coming to rest ?A. nB. 2nC. `(n)/(2)`D. `(n)/(3)`
The M.I. of a solid cylinder about its axis is I. It is allowed to rool down an incline plane without slipping. If its angular velocity at the bottom be `omega`, then kinetic energy of rolling cylinder will beA. `I omega^(2)`B. `(3)/(2)I omega^(2)`C. `2 I omega^(2)`D. `(1)/(2)I omega^(2)`
If a disc of mass 400 gm is rolling on a horizontal surface with uniform speed of 2 m/s, then its rolling kinetic energy will beA. 0.12 JB. 1.2 JC. 120 JD. 12 J
A rigid and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque `tau` on the ring, it stops after making n revolution. After how many revolutions will the disc stop, if the retarding torque on it is also `tau` ?A. nB. 2nC. 4nD. n/2
If the torque acting on a system is zero then, which of the followin quantities is conserced ?A. linear momentumB. angular momentumC. moment of inertiaD. angular velocity
The dimensions of torque are :A. `[L^(3)M^(0)T^(-2)]`B. `[L^(2)M^(2)T^(-3)]`C. `[L^(2)M^(1)T^(-2)]`D. `[L^(2)M^(-1)T^(-3)]`

A roller in a printing press turns through an angle `theta=3t^(2)-t^(3) rad`. (a) Calculate the angular velocity and angular acceleration as a function of time `t`. (b) What is the maximum positive angular velocity and at what time `t` does it occur?

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment