A spinning skater pulls both arms close to the body and spins faster. This happens because
- A.The angular momentum of the skater increases
- B.The moment of inertia decreases, so the angular velocity increases
- C.The torque applied by the skater increases
- D.The mass of the skater decreases
Correct answer
Explanation
The correct answer is B, the moment of inertia decreases, so the angular velocity increases. Moment of inertia is the sum of each bit of mass multiplied by the square of its distance from the axis, so drawing the arms in reduces it. Since no external torque acts about the vertical axis, angular momentum, the product of moment of inertia and angular velocity, stays constant, and a smaller moment of inertia must be matched by a larger angular velocity. Option A is wrong because angular momentum is conserved and does not increase; that is precisely the principle at work. Option C is wrong because the skater applies internal muscular forces, not an external torque about the axis of spin. Option D is wrong because mass cannot change; only its distribution about the axis does. A diver tucking the body in mid air uses the same principle.
Read the full article: Centre of Gravity, Torque and Equilibrium: Exam Notes
Practice Questions
View allWhat is the SI unit of torque?
- A.Newton
- B.Newton metre
- C.Newton per metre
- D.Joule per second
Show answer
Torque is the product of a force and the perpendicular distance of its line of action from the axis of rotation, so its unit is the unit of force multiplied by the unit of length, the newton metre, and its dimensional formula is M L squared T to the power…
Read the full explanation →Three forces acting on a rigid body are represented in magnitude, direction and line of action by the three sides of a triangle taken in order. The forces are equivalent to a couple whose moment is equal to
- A.Thrice the area of the triangle
- B.Twice the area of the triangle
- C.The area of the triangle
- D.Half the area of the triangle
Show answer
When three forces are represented by the sides of a triangle taken in order, their vector sum is zero, because the three sides close the triangle, so the body cannot be pushed away; but the lines of action are different, so the system reduces to a couple.
Read the full explanation →The centre of gravity of a uniform circular ring lies
- A.On the ring itself, at any point
- B.At the centre of the ring, outside its material
- C.At one third of the radius from the centre
- D.Nowhere, because a ring has no centre of gravity
Show answer
The centre of gravity is a geometrical point through which the resultant weight of a body acts, and by symmetry that point for a uniform ring is its geometrical centre, which lies in the empty space inside the ring.
Read the full explanation →The torque produced by a force about an axis is maximum when the angle between the force and the arm is
- A.0 degree
- B.45 degrees
- C.90 degrees
- D.180 degrees
Show answer
The magnitude of torque is r into F into the sine of the angle between the arm and the force, and the sine of an angle is largest, equal to one, at 90 degrees, so the whole of the force is then used in turning the body.
Read the full explanation →A long spanner loosens a tight nut more easily than a short one because it
- A.Reduces the force needed by increasing the moment arm
- B.Reduces the friction at the nut
- C.Increases the mass acting on the nut
- D.Changes the direction of the weight of the nut
Show answer
Torque is the product of the force and the perpendicular distance of its line of action from the axis, so the same turning effect can be produced by a smaller force if that distance is made larger; a long handle therefore does the same work with less effort.
Read the full explanation →