What constant torque should be appiled to a disc of mass `10 kg` and diameter `50 cm` so that it acquires an angular velocity of `2pi` rad/s in `4 s` ? The disc is initially at rest and rotates about an axis through the centre of the disc and in a plane perpendicular to the disc.

What constant torque should be appiled to a disc of mass `10 kg` and d

1.	What constant torque should be appiled to a disc of mass `10 kg` and diameter `50 cm` so that it acquires an angular velocity of `2pi` rad/s in `4 s` ? The disc is initially at rest and rotates about an axis through the centre of the disc and in a plane perpendicular to the disc.
Answer» Here, `tau = ? M = 10 kg`, `R = (50)/(2) cm = (1)/(4)m` `omega = 2pi rad//s, t = 4 s, omega_(0) = 0`. Moment of inertia of disc about the given axis `I = (1)/(2)MR^(2)` `alpha = (omega - omega_(0))/(t) = (2pi - 0)/(4) = (pi)/(2) rad//s^(2)` `tau = I alpha = (1)/(2) MR^(2) xx (pi)/(2)` `= (pi)/(4) xx 10 ((1)/(4))^(2) = (110)/(224) = 0.49 N-m`

Discussion

No Comment Found

Related InterviewSolutions

What is the position vector of centre of mass of two particles of equal masses ?
Consider a two particle system with particles having masses `m_1 and m_2` if the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle is moved, so as to keep the center of mass at the same position?A. `d`B. `(m_(2)//m_(1))d`C. `[m_(1)//(m_(1) + m_(2))]d`D. `(m_(1)//m_(2))d`
By convention, anticlockwise moments are ………and…………are taken as…………. .
As shown in Fig. the two sides of a step ladder `BA` and `CA` are `1.6 m` long and hinged at `A`. A rope `DE, 0.5 m` is tied half way up. A weight `40 kg` is suspended from a point `F, 1.2 m` from B along the ladder` BA`. Assuming the floor to be fricionless and neglecting the weight of the ladder, find the tension in the rope and forces exerted by the floor on the ladder. (Take `g = 9.8 m//s^(2))` (Hint. Consider the eqilibrium of each side of the ladder separately.)
A uniform square plate and a disc having same mass per unit area are kept in contact as shown in Fig. The side of square and diameter of circle are both equal to `L`. Locate the position of centre of mass of the system w.r.t. the centre of the square.
A disc of radius `0.5 m` is rotating about an axis passing through its centre and perpendicular to its plane. A tangential force of `2000 N` is applied to bring the dics to rest `2 s`. Calculate its abgular momentum.
A body of moment of inertia `0.5 kg m^(2)` is rotating about a given axis at the rate `1 rps`. What is kinetic energy of rotation of the body about that axis ?
A cylinder of length `20 cm` and radius `10 cm` is rotating about its central axis at an angular speed of `100 rad//s`. What tangential force will stop the cylinder at a unifrom rate is `10 s` ? Given moment of inertia of the cylinder about its axis of rotation is `8.0 kg m^(2)`.
A dics rotates about the central axis starting from rest and accelerates with constant angular accelertion. At one time, it is rotating at `10 rps` , `60` revoluting later, its angular speed is `15rps`. Calculate (i) angular acceleration (ii) time required to complate `60` revols (iii) the time required to reach `10 rev//sec` angular speed and (iv) number of revoluting from rest until the time the disc reaches `10rps` angular speed.
A Meery -go-round, made of a ring-like plarfrom of radius `R and mass M`, is revolving with angular speed `omega`. A person of mass `M` is standing on it. At one instant, the person jumps off the round, radially awaay from the centre of the round (as see from the round). The speed of the round after wards isA. `2 omega`B. `omega`C. `omega//2`D. `0`

What constant torque should be appiled to a disc of mass `10 kg` and diameter `50 cm` so that it acquires an angular velocity of `2pi` rad/s in `4 s` ? The disc is initially at rest and rotates about an axis through the centre of the disc and in a plane perpendicular to the disc.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment