Target: 10 Questions in 10 minutes

An IB Physics data booklet is helpful

 1. The quantities and formulas used in rotational dynamics are equivalent to the quantities and formulas used for linear motion. The angle Θ in rotation is equivalent to the displacement s in linear motion.

Which of the following symbols are used for the rotational equivalent to mass m and velocity v?

mass m velocity v
A
 I α
B
 I ω
C
 τ α
D
 τ ω

2. The diagram shows 3 weights on a light beam, placed on a pivot at the midpoint.

Torque on a balanced beam with 3 weights

  

What is the torque acting on the system?

  • A. 20 N cm clockwise
  • B. 40 N cm anticlockwise
  • C. 60 N cm anticlockwise
  • D. 90 N cm anticlockwise

3. In the diagram below, a heavy bar of mass 2 kg and length 1.2 m supports another mass of 2 kg as shown. The bar is fastened to a rotating pivot at one end and is in rotational equilibrium.

Torque on a heavy balanced beam

  

What is the approximate tension T in the supporting wire?

  • A. 6 N
  • B. 36 N
  • C. 40 N
  • D. 60 N
4. A steel sphere of radius r has a moment of inertia I given by the equation I = 2/5 mr2.
What is the moment of inertia of a steel sphere with double the radius?
  • 4I
  • 8I
  • 16I
  • 32I

 

5-7. An 8 kg point mass is moving around in a circular path on the end of a beam of negligible mass and length 50 cm. The linear velocity v of the mass is 2 ms-1.

For this rotating system, find..

 rotation of mass on light beam

5. the moment of inertia:

  • A. 2 kg m2
  • B. 20000 kg m2
  • C. 4 kg m2
  • D. 40000 kg m2

6. the rotational kinetic energy:

  • A. 4 J
  • B. 8 J
  • C. 16 J
  • D. 32 J

7. the angular momentum:

  • A. 2 kg m2 s-1
  • B. 4 kg m2 s-1
  • C. 8 kg m2 s-1
  • D. 16 kg m2 s-1

8-10: A student is investigating cylinders rolling down a slope. Two shapes are compared: A solid cylinder and a hollow cylinder. Both have the same length, mass and radius.

solid and hollow cylinders and moment of inertia

 

8. Which of the cylinders has the highest moment of inertia and density?

Highest moment of inertia Highest density material
A
 solid cylinder solid cylinder
B
 solid cylinder hollow cylinder
C
 hollow cylinder solid cylinder
D
 hollow cylinder hollow cylinder

9. The solid cylinder rolls down the slope without slipping at a constant linear velocity v.
Here are three statements about the motion:

I. The moment of inertia of the cylinder is proportional to the linear velocity
II. The angular velocity is proportional to the linear velocity
III. The angular acceleration is zero.

  

Which of these statements are correct?

  • A. I and II
  • B. II and III
  • C. I and III
  • D. I, II and III
10. How is the instantaneous velocity of the top edge of the cylinder ve related to the linear velocity of the centre of the cylinder vc ?
  • A. ve = ½ vc
  • B. ve = vc
  • C. ve = √2 vc
  • D. ve = 2 vc