Q10. Rotational Motion

1. A wheel of diameter 3.0 cm has a 4.0 m cord wrapped

around its periphery. Starting from rest, the wheel is given

a constant angular acceleration of 2 rad/s2. The cord will

unwind in:

1. 0.82 s

2. 2.0 s

3. 8.0 s

4. 16 s

5. 130 s

4

0.03 / 2

s m

r m

16.3t s

2 2 21 12 /

2 2t rad s t

d = 3 cm

L = 4 m = 2 rad/s2

2. String is wrapped around the periphery of a 5.0-cm radius

cylinder, free to rotate on its axis. The string is pulled

straight out at a constant rate of 10 cm/s and does not slip on

the cylinder. As each small segment of string leaves the

cylinder, its velocity changes by:

1. 0

2. 0.010 m/s2

3. 0.020 m/s2

4. 0.10 m/s2

5. 0.20 m/s2

2220.1 /

0.2 /0.05

m sva m s

r m

r = 5 cm

v = 10 cm/s

3. A pulley with a radius of 3.0 cm and a rotational inertia of

4.5 × 10–3 kg m2 is suspended from the ceiling. A rope

passes over it with a 2.0-kg block attached to one end and a

4.0-kg block attached to the other. The rope does not slip

on the pulley. When the velocity of the heavier block is 2.0

m/s the total kinetic energy of the pulley and blocks is:

1. 2.0 J

2. 4.0 J

3. 14 J

4. 22 J

5. 28 J

2

2 3 21 1 2.0 /4.0 2.0 2.0 / 4.5 10

2 2 0.03

m sKE kg kg m s kg m

m

Everything is moving with speed 2.0 m/s.

22 J

r = 3 cmI = 4.5×103 kg m2

M = 4.0 kgV = 2.0 m/s

m = 2.0 kg

22 21 1 1

2 2 2

vKE mv I I

r

4. A and B are two solid cylinders made of aluminum. Their

dimensions are shown. The ratio of the rotational inertia of

B to that of A about the common axis X─X' is:

1. 2

2. 4

3. 8

4. 16

5. 32

2 4 4

42 4

1

322 2A A A A A

B B B B B

I M R L R LR

I M R L R L R

Moment of inertia = M R2,

where is a geometric

factor.

5. A 16 kg block is attached to a cord that is wrapped around the

rim of a flywheel of diameter 0.40 m and hangs vertically, as

shown. The rotational inertia of the flywheel is 0.50 kg × m2.

When the block is released and the cord unwinds, the

acceleration of the block is:

1. 0.15 g

2. 0.56 g

3. 0.84 g

4. g

5. 1.3 g

mg T ma

aT r I I

r

Let T be the tension in the cord

2

amg I ma

r

2 2

1

1

mga g

I Im

r m r

2

2

10.56

0.501

16 0.20

g gkg m

kg m

I = 0.50 kg × m2

T

m g a

T

6. A disk starts from rest and rotates around a fixed axis,

subject to a constant net torque. The work done by the

torque during the second 5 s is ______ as the work done

during the first 5 s.

1. the same

2. three times as much

3. one third as much

4. four times as much

5. one fourth as much

Work done under constant torque is proportional to angular dispacement .

Starting from rest, t2 .

21 5

2 22 5

5 25 1

10 5 75 3st s

nd s

W

W

20

1

2W d I I t t

τ θ

7. A small disk of radius R1 is mounted coaxially with a larger disk of

radius R2. The disks are securely fastened to each other and the

combination is free to rotate on a fixed axle that is perpendicular to a

horizontal frictionless table top as shown in the overhead view below.

The rotational inertia of the combination is I. A string is wrapped

around the larger disk and attached to a block of mass m, on the table.

Another string is wrapped around the smaller disk and is pulled with a

force as shown. The acceleration of the block is :

1. R1 F / m R2

2. R1 R2 F / ( I – mR22 )

3. R1 R2 F / ( I + mR22 )

4. R1 R2 F / ( I – mR1R2 )

5. R1 R2 F / ( I + mR1R2 )

2 12

aT R F R I

R

1 1 2

22

22

F R F R Ra

I I mRmRR

T ma

TT

R1

R2a