Rotational Motion

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What is the time period of a compound pendulum?

T = 2π √(L^4/g)

T = 2π √(L^2/g)

T = 2π √(L^3/g)

T = 2π √(L/g) (correct)

What is the radius of gyration of a ring about a parallel axis passing through its centre?

R/2

R/√2

R (correct)

2R

What is the time period of a compound pendulum of length 2R and radius of gyration R/2?

2π √(4R/g)

2π √(R/g)

2π √(2R/g) (correct)

2π √(R/2g)

What is the velocity of a solid sphere that rolls down an inclined plane of length 1.4 m, starting from rest?

1.4 m/s Signup and view all the answers

What is the relation between the velocities of a solid sphere that rolls down an inclined plane and one that slides down the plane without friction?

v1 ≠ v2 Signup and view all the answers

What is the downwards acceleration of a point mass tied to a string wound around a solid body, when released?

g(I + mR)/(I + 2mR) Signup and view all the answers

What is the expression for the velocity of a point mass tied to a string wound around a solid body, when released?

√(2gh(I + mR)/(I + 2mR)) Signup and view all the answers

What is the moment of inertia of a uniform rod of mass M and length L about an axis through its centre?

$\frac{ML^2}{12}$ Signup and view all the answers

What happens to the angular momentum of the system when the beads reach the ends of the rod?

It remains constant Signup and view all the answers

What is the torque responsible for the rotation of the rod?

No torque Signup and view all the answers

What is the type of motion exhibited by the rod?

Rotational motion Signup and view all the answers

What is the angular velocity of the automobile engine in Problem 42?

30 rad/s Signup and view all the answers

What is the moment of inertia of the body in Problem 43?

3 kg-m2 Signup and view all the answers

If the rotational kinetic energy of the body in Problem 43 is 12 J, what is its angular velocity?

2 rad/s Signup and view all the answers

If the radius of gyration of a body is 0.5 m, what is its moment of inertia if it has a mass of 10 kg?

1.25 kg-m2 Signup and view all the answers

If the angular momentum of a rotating body is increased by 200%, then its rotational kinetic energy will be increased by

800% Signup and view all the answers

A ring, a solid sphere, and a thin disc of different masses rotate with the same kinetic energy. Equal torques are applied to stop them. Which will make the least number of rotations before coming to rest?

All will make the same number of rotations Signup and view all the answers

The angular velocity of a body is ω = 2ˆi + 3ˆj + 4kˆ and a torque τ = ˆi + 2ˆj + 3kˆ acts on it. The rotational power will be

20 W Signup and view all the answers

A flywheel of moment of inertia 0.32 kg-m² is rotated steadily at 120 rad/sec by a 50 W electric motor. The kinetic energy of the flywheel is

2304 J Signup and view all the answers

If the moment of inertia of a rotating body is increased by 50%, then its angular velocity will be decreased by

33% Signup and view all the answers

What is the rotation kinetic energy of a body rotating about a fixed axis?

½Iω² Signup and view all the answers

What is the rate of change of kinetic energy defined as?

Power Signup and view all the answers

What is the expression for the moment of inertia of a body about a fixed axis?

mr² Signup and view all the answers

What is the ratio of rotational kinetic energy to translational kinetic energy for a spinning body?

K²:1 Signup and view all the answers

When a body rotates about a fixed axis, what is the nature of motion of its constituent particles?

Circular Signup and view all the answers

If the moment of inertia of a rotating body is increased by 25%, then its radius of gyration will be increased by

12.5% Signup and view all the answers

A torque of 10 Nm is applied to a body rotating at 5 rad/s. If the angular velocity of the body increases by 2 rad/s, what is the change in its rotational kinetic energy?

40 J Signup and view all the answers

A solid sphere of radius 0.2 m is rotating at 10 rad/s about a fixed axis. What is its angular velocity about a parallel axis passing through its centre?

10 rad/s Signup and view all the answers

If the angular velocity of a rotating body is increased by 50%, then its rotational kinetic energy will be increased by

225% Signup and view all the answers

A flywheel of moment of inertia 0.5 kg-m² is rotated steadily at 150 rad/s by a 75 W electric motor. What is the torque delivered by the motor?

25 Nm Signup and view all the answers