Do now:Why does a tight-rope walkeruse a long pole?

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Friday, April 21, 2023

• Just as force causes linear acceleration, torque causes angular acceleration.

• I is the “rotational inertia” which measures how hard it is to get an object spinning

I Compare with F = ma

2I mr• Units: kg m2

• Rotational inertia depends on:– mass– how the mass is distributed about the axis of rotation

2 21 1 2 2 ...m r m r

20cm

5kg 5kgI = ?

Board notes

Examples of Inertia’s

2

2

2

1

2

2

5

I mr

I mr

I mr

Solid CylinderSolid Cylinder

Hollow CylinderHollow Cylinder

Solid SphereSolid Sphere

Board notes

Example:Tom wants to push his friends on a roundabout. Will he find it easier if they all stand in the centre or on the outer edge? Why?

• Total mass is the same in both cases• But rotational inertia is smaller when all the mass is nearer

the centre of rotation, so easier to push• Watch ice skating world record (15s) + demo

“Classic” Example:A mass of 0.18kg is used to accelerate a wheel of radius

0.20m.The mass accelerates downwards at 1.2ms-2

a) Calculate the tension force in the stringb) Calculate the torque on the wheelc) Calculate the angular acceleration of the wheeld) Calculate the rotational inertia of the wheel

Do Activity 9B, Q1-4