A body rotates about a fixed axis with an angular acceleration of 1 rad/sec2. Through what does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s?

Collegedunia Team

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The equation of rotational motion for constant angular acceleration is given by

ω_f² = ω_i² + 2αθ

⇒ θ = $\frac{\omega_f^2 - \omega_i^2}{2 \alpha}$

Where

ω_f = final angular velocity
ω_i = initial angular velocity
α = angular acceleration
θ = angular displacement of the body during the time in which its angular velocity

Changes from ω_ito ω_f

Given,

Initial angular velocity of the fan, ω_i = 5 rad/s

final angular velocity of the fan, ω_f = 15 rad/s

Angular acceleration, α = 1 rad/sec²

Using the equation of rotational motion, angular displacement of the fan, is given by

θ = $\frac{15^2-5^2}{2 \times 1}$ = $\frac{225-25}{2}$ = 100 rad

Hence, the body rotates angular displacement of 100 rad during the time in which its angular velocity increases from 5 rad/s to 15 rad/s.

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A boy of mass 50 kg is standing at one end of a, boat of length 9 m and mass 400 kg. He runs to the other, end. The distance through which the centre of mass of the boat boy system moves is

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A body rotates about a fixed axis with an angular acceleration of 1 rad/sec2. Through what does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s?

CBSE CLASS XII Related Questions

1. A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field ?inside the spherejust outside the sphereat a point 18 cm from the centre of the sphere?

2. A convex lens of glass is immersed in water compared to its power in air, its power in water will

3. A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is

4. A boy of mass 50 kg is standing at one end of a, boat of length 9 m and mass 400 kg. He runs to the other, end. The distance through which the centre of mass of the boat boy system moves is

5. A capillary tube of radius r is dipped inside a large vessel of water. The mass of water raised above water level is M. If the radius of capillary is doubled, the mass of water inside capillary will be

6. In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10–3 m2 and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

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Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A spherical conductor of radius 12 cm has a charge of 1.6 × 10^–7C distributed uniformly on its surface. What is the electric field ?
inside the sphere
just outside the sphere
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A convex lens of glass is immersed in water compared to its power in air, its power in water will

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A capillary tube of radius r is dipped inside a large vessel of water. The mass of water raised above water level is M. If the radius of capillary is doubled, the mass of water inside capillary will be

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In a parallel plate capacitor with air between the plates, each plate has an area of 6 × 10^–3 m² and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?