Question 1

A solid disk of radius $$0.10\ \mathrm{m}$$ and mass $$2.0\ \mathrm{kg} is $$spinning at $$1200\ \mathrm{rpm} at$$ $$t=0. It is $$then subjected to a constant frictional torque, causing it to stop in $$20.0\ \mathrm{s}. $$What is the total number of revolutions made before it comes to rest?

Accepted Answer

$$400$$

Question 2

Consider a point on the edge of a $$0.10\ \mathrm{m}$$ radius disk rotating at $$1200\ \mathrm{rpm}. $$What is the magnitude of the tangential acceleration of the point as the disk slows to a stop in $$20.0\ \mathrm{s}$$?

Accepted Answer

$$0.63\ \mathrm{$$rad/s^2$$}$$

Question 3

What is the magnitude of the disk's rotational torque if its moment of inertia is $$I = \frac{1}{2}MR^2$ and it slows from 1200$$\ \mathrm{rpm}$$ to rest in 20.0$$\ \mathrm{s}$$?

Accepted Answer

$$0.20\ \mathrm{N\cdot m}$$

Question 4

Which of the following statements about angular momentum is TRUE?

Accepted Answer

Angular momentum is conserved only when the net external torque is zero.

Question 5

A $$4.0\ \mathrm{kg}$$ weight is placed on a spring scale on a fictional planet. The scale reads $$20\ \mathrm{N}. $$What is the acceleration due to gravity on this planet?

Accepted Answer

$$5.0\ \mathrm{m/s^2$}$$

Question 6

A solid sphere of mass $$2.0\ \mathrm{kg}$$ and radius $$0.10\ \mathrm{m}$$ rolls down a $$1.0\ \mathrm{m}$$ high incline without slipping. What is its speed at the bottom?

Accepted Answer

$$3.09\ \mathrm{m/s}$$

Question 7

A $$0.10\ \mathrm{m}$$ diameter turntable (solid disk) rotates at $$60\ \mathrm{rpm}. $$What is the angular speed in $$\mathrm{rad/s}$$?

Accepted Answer

$$9.42\ \mathrm{rad/s}$$

Question 8

A $$0.10\ \mathrm{m}$$ diameter turntable rotates at $$60\ \mathrm{rpm}. $$What is the magnitude of the total (tangential plus centripetal) acceleration of a point on the rim?

Accepted Answer

$$0.60\ \mathrm{m/s^2$}$$

Question 9

A $$0.10\ \mathrm{m}$$ diameter turntable (solid disk) rotates at $$60\ \mathrm{rpm}. If $$the turntable is slowed by friction so that its angular speed decreases by $$4.44\%$$ per second, what is the angular acceleration?

Accepted Answer

$$-0.42\ \mathrm{$$rad/s^2$$}$$

Question 10

A block of mass $$m_1$$ and a block of mass $$m_2$$ are connected by a massless string that passes over a solid pulley of radius $$R$$ and mass $$M. $$The system is released from rest. What is the acceleration of the system in terms of $$m_1$$, $$m_2$$, $$M$$, and $$g$$?

Accepted Answer

$$a = \frac{(m_1$ - m_2$)g}{m_1$ + m_2$ + \frac{1}{2}M}$$

Question 11

A $$2.0\ \mathrm{kg}$$ mass is attached to a $$0.5\ \mathrm{m}$$ long string and swung in a horizontal circle at $$4.0\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$32\ \mathrm{N}$$

Question 12

A $$0.10\ \mathrm{m}$$ radius disk of mass $$2.0\ \mathrm{kg}$$ rotates at $$1200\ \mathrm{rpm}. $$What is its rotational kinetic energy?

Accepted Answer

$$12\ \mathrm{J}$$

Question 13

A $$0.10\ \mathrm{m}$$ radius disk of mass $$2.0\ \mathrm{kg}$$ rotates at $$1200\ \mathrm{rpm}. If $$the disk is brought to rest by a constant frictional torque, what is the work done by friction?

Accepted Answer

$$12\ \mathrm{J}$$

Question 14

A $$0.10\ \mathrm{m}$$ radius disk of mass $$2.0\ \mathrm{kg}$$ rotates at $$1200\ \mathrm{rpm}. $$What is its angular momentum?

Accepted Answer

$$2.5\ \mathrm{kg\cdot m^2$/s}$$

Question 15

A $$0.10\ \mathrm{m}$$ radius disk of mass $$2.0\ \mathrm{kg}$$ rotates at $$1200\ \mathrm{rpm}. If a $$second identical disk is dropped onto it and sticks, what is the final angular speed?

Accepted Answer

$$600\ \mathrm{rpm}$$

Question 16

A $$0.10\ \mathrm{m}$$ radius disk of mass $$2.0\ \mathrm{kg}$$ rotates at $$1200\ \mathrm{rpm}. If a $$second identical disk is dropped onto it and sticks, what is the final rotational kinetic energy?

Accepted Answer

$$6\ \mathrm{J}$$

Question 17

A $$0.10\ \mathrm{m}$$ radius disk of mass $$2.0\ \mathrm{kg}$$ rotates at $$1200\ \mathrm{rpm}. If a $$second identical disk is dropped onto it and sticks, what fraction of the initial kinetic energy is lost?

Accepted Answer

$$0.5$$

Question 18

A $$0.10\ \mathrm{m}$$ radius disk of mass $$2.0\ \mathrm{kg}$$ rotates at $$1200\ \mathrm{rpm}. If a $$second identical disk is dropped onto it and sticks, what is the change in angular momentum?

Accepted Answer

$$0$$

Rotation of a Rigid Body and Angular Momentum: Study Notes and Worked Examples

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