Given:
Mass of the flywheel, \( m = 20 \, {kg} \)
Radius, \( r = 100 \, {mm} = 0.1 \, {m} \)
Angular velocity, \( \omega = 600 \, {rpm} = \frac{600 \times 2\pi}{60} = 62.83 \, {rad/s} \)
Time to stop, \( t = 3.14 \, {s} \)
Coefficient of friction, \( \mu = 0.1 \)
Step 1: Calculate the angular deceleration (\( \alpha \)) The flywheel comes to rest in 3.14 s, so the angular deceleration is: \[ \alpha = \frac{\Delta \omega}{t} = \frac{0 - 62.83}{3.14} = -20 \, {rad/s}^2 \] The magnitude of angular deceleration is \( 20 \, {rad/s}^2 \).
Step 2: Calculate the torque (\( \tau \)) The torque required to stop the flywheel is: \[ \tau = I \alpha \] where \( I \) is the moment of inertia of the flywheel. For a solid disk: \[ I = \frac{1}{2} m r^2 = \frac{1}{2} \times 20 \times (0.1)^2 = 0.1 \, {kg m}^2 \] Thus, the torque is: \[ \tau = 0.1 \times 20 = 2 \, {Nm} \] Step 3: Calculate the frictional force (\( F \)) The torque is also given by: \[ \tau = F \cdot r \] Solving for \( F \): \[ F = \frac{\tau}{r} = \frac{2}{0.1} = 20 \, {N} \] However, considering the coefficient of friction \( \mu = 0.1 \), the normal force \( N \) required to produce this frictional force is: \[ F = \mu N \implies N = \frac{F}{\mu} = \frac{20}{0.1} = 200 \, {N} \] Thus, the force to be applied against the flywheel is 200 N.
Final Answer: 200 N
A uniform circular disc of radius \( R \) and mass \( M \) is rotating about an axis perpendicular to its plane and passing through its center. A small circular part of radius \( R/2 \) is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.
A metal rod of 50 cm length is clamped at its midpoint and is set to vibrations. The density of that metal is \( 2 \times 10^3 \, {kg/m}^3 \).
Young's modulus of that metal is \( 8 \times 10^8 \, {Nm}^2 \). The fundamental frequency of the vibration is
Two statements are given below
Statement I: Benzanamine can be prepared from phthalimide.
Statement II: Benzanamine is less basic than phenyl methanamine.
What are X and Z in the following reaction sequence?
What is Y in the following reaction sequence?
Observe the following set of reactions:
Correct statement regarding Y and B is:
What is X in the following reaction?