A drum with mass moment of inertia 20.0 kg·m² is driven by a constant torque of 99 N·m from rest. Find α and the angular speed after 6.0 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 99/20.0 = 4.950 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 4.950(6.0) = 29.70 rad/s$$

5. Convert

   $$\omega = 283.6 rpm$$

Why the other options are there

• 1,980 rad/s² (multiplied instead of divided)
• 4.73 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation

A drum with mass moment of inertia 21.0 kg·m² is driven by a constant torque of 165 N·m from rest. Find α and the angular speed after 9.5 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 165/21.0 = 7.857 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 7.857(9.5) = 74.64 rad/s$$

5. Convert

   $$\omega = 712.8 rpm$$

Why the other options are there

• 3,465 rad/s² (multiplied instead of divided)
• 11.88 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation

A drum with mass moment of inertia 4.0 kg·m² is driven by a constant torque of 186 N·m from rest. Find α and the angular speed after 9.5 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 186/4.0 = 46.500 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 46.500(9.5) = 441.8 rad/s$$

5. Convert

   $$\omega = 4,218 rpm$$

Why the other options are there

• 744.0 rad/s² (multiplied instead of divided)
• 70.31 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation

A drum with mass moment of inertia 26.5 kg·m² is driven by a constant torque of 119 N·m from rest. Find α and the angular speed after 9.0 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 119/26.5 = 4.491 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 4.491(9.0) = 40.42 rad/s$$

5. Convert

   $$\omega = 385.9 rpm$$

Why the other options are there

• 3,154 rad/s² (multiplied instead of divided)
• 6.43 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation

A drum with mass moment of inertia 28.0 kg·m² is driven by a constant torque of 187 N·m from rest. Find α and the angular speed after 5.5 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 187/28.0 = 6.679 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 6.679(5.5) = 36.73 rad/s$$

5. Convert

   $$\omega = 350.8 rpm$$

Why the other options are there

• 5,236 rad/s² (multiplied instead of divided)
• 5.85 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation

A drum with mass moment of inertia 23.5 kg·m² is driven by a constant torque of 183 N·m from rest. Find α and the angular speed after 5.5 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 183/23.5 = 7.787 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 7.787(5.5) = 42.83 rad/s$$

5. Convert

   $$\omega = 409.0 rpm$$

Why the other options are there

• 4,301 rad/s² (multiplied instead of divided)
• 6.82 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation

A drum with mass moment of inertia 15.0 kg·m² is driven by a constant torque of 180 N·m from rest. Find α and the angular speed after 5.5 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 180/15.0 = 12.000 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 12.000(5.5) = 66.00 rad/s$$

5. Convert

   $$\omega = 630.3 rpm$$

Why the other options are there

• 2,700 rad/s² (multiplied instead of divided)
• 10.50 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation

A drum with mass moment of inertia 5.0 kg·m² is driven by a constant torque of 182 N·m from rest. Find α and the angular speed after 3.0 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 182/5.0 = 36.400 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 36.400(3.0) = 109.2 rad/s$$

5. Convert

   $$\omega = 1,043 rpm$$

Why the other options are there

• 910.0 rad/s² (multiplied instead of divided)
• 17.38 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation

A drum with mass moment of inertia 25.5 kg·m² is driven by a constant torque of 156 N·m from rest. Find α and the angular speed after 4.0 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 156/25.5 = 6.118 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 6.118(4.0) = 24.47 rad/s$$

5. Convert

   $$\omega = 233.7 rpm$$

Why the other options are there

• 3,978 rad/s² (multiplied instead of divided)
• 3.89 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation

A drum with mass moment of inertia 9.0 kg·m² is driven by a constant torque of 10 N·m from rest. Find α and the angular speed after 7.5 s.

Start with the thinking

• Rotational analogue of F = ma is M = Iα.
• Constant torque gives constant angular acceleration.

Step-by-step solution

1. Rotational equation

   $$M = I\alpha$$

2. Substituting

   $$\alpha = 10/9.0 = 1.111 rad/s^{2}$$

3. Angular speed — ω = ω₀ + αt

4. Substituting

   $$\omega = 0 + 1.111(7.5) = 8.33 rad/s$$

5. Convert

   $$\omega = 79.6 rpm$$

Why the other options are there

• 90.0 rad/s² (multiplied instead of divided)
• 1.33 rad/s (revolutions confused with radians)

Reference: FE Reference Handbook — Dynamics → Rigid Body Rotation